Causality, Ensemble Invariance, and Black-Hole Perturbations: Prof. Dr. ˙Izzet Sakallı on the KSS Bound, Thermodynamic Topology, and Quasinormal-Mode Inference (3)
Scott Douglas Jacobsen (Email: scott.jacobsen2026@gmail.com)
Publisher, In-Sight Publishing
Fort Langley, British Columbia, Canada
Received: October 25, 2025
Accepted: January 8, 2026
Published: February 22, 2026
Abstract
This interview excerpt with Prof. Dr. ˙Izzet Sakallı synthesizes several live problems at the interface of black-hole physics, holography, thermodynamics, and computational method. First, it addresses whether thermal fluctuations can undermine the Kovtun–Son–Starinets (KSS) bound on the shear-viscosity-to-entropy-density ratio in quantum-corrected AdS black holes. Sakallı argues that the bound is formulated for ensemble-averaged thermodynamic quantities rather than instantaneous microstates, and that causality constraints and fluctuation–dissipation structure prevent genuine violations even when entropy and horizon data fluctuate. Quantum corrections are presented as shifting the numerical value of the bound in controlled ways rather than eliminating the existence of a lower bound. Second, the excerpt proposes an operational, coordinate-independent notion of “thermodynamic topology,” treating equilibrium state space as a manifold equipped with geometric structures (metrics, curvature, and topological invariants such as winding numbers) that classify critical points and phase transitions, with ensemble changes understood via Legendre transformations on a broader thermodynamic phase space. Third, Sakallı outlines a phenomenological unification of linear dilaton, Newman–Unti–Tamburino, and Bardeen geometries, emphasizing their shared “hair,” nonstandard asymptotics, modified thermodynamics, and comparable signatures in geodesic structure and observables such as shadows and inspiral waveforms. Finally, the excerpt compares higher-order WKB approaches and neural networks for extracting quasinormal modes, identifying the main methodological pitfalls—convergence, coordinate and boundary-condition sensitivity versus data dependence, extrapolation risk, and interpretability—and motivating hybrid strategies that combine physical transparency with computational speed.
Keywords
AdS/CFT, Asymptotics, Bardeen black holes, Boundary conditions, Black hole hair, Black hole shadows, Causality constraints, Compactification, Coordinate independence, Curvature (thermodynamic), Dilaton fields, Ensemble averaging, Euler characteristic, Extended phase space, Extrapolation risk, Fluctuation–dissipation theorem, Gauss–Bonnet gravity, Geodesics, Gibbs free energy, Grand canonical ensemble, Gravitational waves, Heavy-ion collisions, Helmholtz free energy, Higher-derivative corrections, Holography, Interpretability, ISCO (innermost stable circular orbit), KSS bound, Legendre transformations, Linear dilaton black holes, LIGO constraints, Machine learning, Microcanonical ensemble, Misner string, Neural networks, Newman–Unti–Tamburino (NUT) spacetime, Nonlinear electrodynamics, Overfitting, Phase transitions, Photon sphere, Pietist discipline, Quark–gluon plasma, Quasinormal modes, Quantum corrections, Shear viscosity, Symplectic structure, Thermal fluctuations, Thermodynamic manifold, Thermodynamic metric, Thermodynamic topology, Topological charge, Transport coefficients, Van der Waals analogy, Viscosity-to-entropy ratio, Winding number, WKB approximation
Introduction
Modern black-hole physics is no longer a single subject so much as a crowded intersection: holography links gravity to strongly coupled fluids; extended thermodynamics reframes spacetime constants as state variables; and observational astronomy increasingly constrains “beyond Kerr–Newman” possibilities. In this excerpt, Prof. Dr. ˙Izzet Sakallı engages several of these frontiers through a unifying methodological concern: which statements are invariant, operationally meaningful, and robust under corrections—whether those corrections are quantum, thermal, coordinate-based, or computational.
The discussion begins with the Kovtun–Son–Starinets bound, a conjectured lower limit on the ratio of shear viscosity to entropy density that emerges naturally from AdS/CFT calculations. Sakallı addresses a common worry in quantum-corrected AdS black holes: if entropy and horizon properties fluctuate, could momentary configurations appear to violate the bound? He frames the bound as a statement about coarse-grained thermodynamic quantities, protected by causality and by the structured relation between fluctuations and dissipation, and he argues that quantum corrections typically deform the bound’s value rather than abolish the existence of a bound.
The excerpt then shifts from bounds to classification, proposing an operational definition of thermodynamic topology that is explicitly coordinate-independent. Equilibrium state space is treated as a manifold where thermodynamic potentials define fields, critical points behave as topological defects, and invariants such as winding numbers provide a stable language for phase transitions. Because ensemble choice changes which variables are held fixed, Sakallı emphasizes a geometric formulation in which Legendre transformations are understood as coordinate changes within a broader phase space equipped with ensemble-independent structure, allowing invariants to remain well-posed across descriptions.
From there, the interview broadens to a phenomenological comparison of three nonstandard black-hole families—linear dilaton, NUT, and Bardeen—highlighting the shared presence of additional “hair,” altered asymptotics, and modified thermodynamics and geodesics, with implications for shadows, accretion signatures, and gravitational-wave observables. The excerpt closes with a methodological contrast between higher-order WKB techniques and neural networks for computing quasinormal modes, weighing physical interpretability and controlled approximation against speed, data dependence, and extrapolation risk, and motivating hybrid strategies that preserve both exploration and rigor.
Main Text (Interview)
Title: Causality, Ensemble Invariance, and Black-Hole Perturbations: Prof. Dr. ˙Izzet Sakallı on the KSS Bound, Thermodynamic Topology, and Quasinormal-Mode Inference (3)
Interviewer: Scott Douglas Jacobsen
Interviewees: Prof. Dr. İzzet Sakallı
Professor Izzet Sakallı is a theoretical physicist at Eastern Mediterranean University whose research bridges quantum mechanics, general relativity, and observational astronomy. With over 180 publications exploring black hole thermodynamics, modified gravity theories, and quantum corrections to spacetime, his work sits at the exciting frontier where abstract mathematics meets observable reality. In this interview, he discusses the challenges of testing exotic gravity theories, the quest to observe quantum effects in astrophysical systems, and what the next generation of telescopes and gravitational wave detectors might reveal about the quantum nature of spacetime.
Scott Douglas Jacobsen: Which shadow features best test Lorentz-violating backgrounds once plasma and accretion-flow systematics are in cluded?
Professor Izzet Sakallı: The Event Horizon Telescope’s stunning images of M87* and Sagittarius A* opened an unprece dented window for testing fundamental physics. These images show a bright ring of emission surrounding a dark shadow—the gravitational silhouette of the black hole. But extracting con straints on exotic physics requires carefully separating genuine signatures of modified spacetime from astrophysical contamination.
Lorentz invariance—the principle that physical laws don’t depend on your orientation or ve locity—is a cornerstone of both special and general relativity. Various approaches to quantum gravity predict potential violations at high energies or in strong gravitational fields. These violations would modify how photons propagate, potentially changing the observed shadow.
The challenge is that accretion disks—the hot, ionized material spiraling into black holes—are messy astrophysical environments. The plasma causes Faraday rotation of polarized light, in troduces frequency-dependent delays through dispersion, absorbs some wavelengths while trans mitting others, and Doppler shifts due to its orbital motion. All these effects must be modeled and subtracted to reveal underlying spacetime properties.
The most robust tests use signatures that depend differently on fundamental physics versus astrophysical processes. Multi-wavelength shadow measurements provide one such discriminator. If Lorentz violation affects photon propagation, the shadow size should vary with observing frequency in a specific pattern—different from how plasma effects scale. Observing at 230 GHz, 345 GHz, and potentially infrared wavelengths with the next-generation Event Horizon Telescope would allow separating these effects.
The photon ring—actually a series of nested subrings from photons completing multiple orbits before escaping—offers another powerful probe. The time delay between successive subrings de pends on geodesic motion in the spacetime geometry, largely insensitive to accretion flow details since it’s a geometric effect. Lorentz violation would modify these time delays in characteristic ways.
Polarization patterns provide additional leverage. While plasma Faraday rotation certainly af fects polarization, Lorentz violation can break azimuthal symmetry in distinctive ways. Decom posing the polarization pattern into angular components helps separate astrophysical rotation (which affects all components similarly) from symmetry-breaking physics.
Time variability studies offer yet another approach. Monitoring shadow features over days to months separates quasi-periodic variability from orbital motion, flares and turbulence in the accretion flow, and any secular trends from fundamental physics. If the shadow properties slowly drift in ways inconsistent with astrophysical explanations, that might signal Lorentz violation.
Current EHT observations constrain deviations from general relativity at the ten to twenty percent level. This translates to saying that if Lorentz violation exists, its characteristic energy scale must be at least one or two percent of the Planck energy—still far below the Planck scale but better constraints than many other tests achieve.
Future improvements will come from multiple directions. The next-generation EHT adds more telescopes and space-based stations, increasing angular resolution. Higher observing frequencies probe smaller scales. Broader bandwidth improves sensitivity. Perhaps most importantly, coordinated multi-messenger observations—combining radio interferometry with X-ray timing, optical monitoring, and potentially gravitational waves if the black hole is in a binary—would provide complementary information less susceptible to systematic uncertainties.
Jacobsen: What are the limits of the Gauss-Bonnet approach for weak deflection in spacetimes with torsion?
Sakallı: Einstein-dilaton-Gauss-Bonnet gravity represents an important modification of general relativ ity emerging from string theory. The Gauss-Bonnet term involves products of curvature quan tities in a specific combination that’s topologically interesting. In standard four-dimensional spacetime, this term is actually a topological invariant—it doesn’t affect the equations of motion by itself. But when coupled to a dilaton field (a scalar field from string theory), it produces genuine modifications to gravity.
These modifications become significant in strong-field regions near black holes or in the early universe. For weak gravitational fields—like sunlight grazing the Sun—the corrections are typically small but calculable. We can expand solutions perturbatively, treating the Gauss Bonnet term as a small correction to general relativity, and calculate how it affects phenomena like light deflection. However, this approach encounters fundamental difficulties when spacetime possesses torsion.
Torsion represents a twisting of spacetime, a type of geometric structure absent in general relativity but present in some extended theories. Einstein-Cartan theory, for instance, allows spacetime to have both curvature and torsion, with torsion sourced by intrinsic spin of matter.
The difficulty is that the Gauss-Bonnet term is defined for Riemannian geometry—geometry with curvature but no torsion. Generalizing it to spaces with torsion isn’t unique. Multiple inequivalent extensions exist: the Nieh-Yan form, modifications involving the Pontrjagin term, generalizations of the Holst term. These different extensions give different physics, and there’s no obvious principle selecting one over others.
Furthermore, torsion couples to matter fields differently than curvature. For photons—massless spin-one particles—the interaction with torsion is subtle. Traditional geodesic equations must be reconsidered. The very notion of ”geodesic” becomes ambiguous because the connection determining parallel transport includes torsion contributions.
The weak-field expansion faces technical breakdowns in torsion backgrounds. We typically expand the metric as small perturbations around flat spacetime. But when both curvature and torsion are present, the perturbative hierarchy becomes unclear. If torsion is as large as curvature perturbations, our expansion scheme breaks down.
There are also boundary term subtleties. In formulating gravitational theories variationally, boundary terms matter for defining conserved quantities and obtaining correct equations of motion. The Gibbons-Hawking-York boundary term supplements the Einstein-Hilbert action in general relativity. With torsion, additional boundary terms are needed, and they affect asymptotic quantities crucial for calculating observable effects like deflection angles.
Some torsion-Gauss-Bonnet couplings lead to pathologies: faster-than-light propagation, vio lations of causality, or violations of energy conditions guaranteeing stability. These signal the theory’s breakdown rather than providing viable alternatives to general relativity.
Observationally, constraints on torsion in astrophysical contexts are weak. Particle physics experiments provide stronger bounds from spin-dependent effects. But astrophysical torsion contributions must satisfy stringent limits, roughly one part in a billion billion per centimeter from precision tests.
For analyzing light deflection in torsion-rich spacetimes, alternative approaches work better than weak-field expansions. Full numerical ray-tracing through exact solutions avoids perturbative ambiguities. The Newman-Penrose formalism, adapted to non-Riemannian geometry, provides another rigorous framework. Modified Shapiro time delays offer complementary probes less sensitive to expansion scheme choices.
Jacobsen: Which lensing signatures would rule out thin-shell wormholes for compact black-hole mimics?
Sakallı: Wormholes—hypothetical tunnels connecting distant regions of spacetime—have captivated physicists and science fiction writers for decades. While the Schwarzschild solution allows math ematical wormholes, they’re unstable and not traversable. Maintaining a stable, traversable wormhole requires exotic matter violating energy conditions, specifically matter with negative energy density.
Thin-shell wormholes represent a particular construction where exotic matter is confined to a narrow region around the wormhole throat, minimizing the total amount of energy-condition violating material needed. From a distance, such objects might mimic black holes—appearing as compact, massive objects with strong gravitational fields. Distinguishing them observationally is crucial, as finding a wormhole would revolutionize physics.
Several observational signatures could definitively distinguish wormholes from black holes. The most dramatic is gravitational wave echoes. When a gravitational wave rings down after a black hole merger, the signal decays smoothly—the perturbations fall into the singularity. But if the object is a wormhole, perturbations can traverse the throat, reflect off the geometry on the far side, return, and emerge again. This creates periodic echoes in the gravitational wave signal, with the time delay determined by the wormhole’s size and geometry.
Detecting echoes is challenging. The reflected signal is weaker than the initial ringdown, requir ing high signal-to-noise ratio observations. Current searches in LIGO/Virgo data have found no convincing echoes, placing limits on how common wormholes might be if they exist. Future detectors with better sensitivity, particularly Einstein Telescope and Cosmic Explorer, should significantly improve echo searches.
The shadow morphology offers another discriminator. Black holes cast circular (or slightly elliptical for rotating ones) shadows. Wormholes can produce more exotic shadow shapes: non simply-connected topology (hole within hole), asymmetric brightness from different light paths traversing the throat, or chromatic effects if the throat has frequency-dependent properties. The Event Horizon Telescope’s resolution is reaching the point where such features might be detectable for nearby supermassive objects.
Microlensing provides a third signature. When a compact object passes in front of a background star, its gravity acts as a lens, magnifying and distorting the star’s image. Black holes create characteristic magnification curves. Wormholes add complexity: light paths traversing the throat create additional magnification spikes, producing asymmetric light curves distinct from black hole lensing. Large microlensing surveys searching for dark matter or planets could potentially detect such signatures if wormholes exist in our galaxy.
Time delay distributions between multiple images offer another probe. Gravitational lenses create multiple images of background objects arriving at different times. The distribution of these delays depends on the lens’s mass profile. Wormholes’ different internal geometry would create distinctive delay patterns.
Future interferometric observations using nulling techniques could enhance faint photon ring structure while suppressing the bright accretion disk. Wormholes’ multiple light traversal paths would create interference patterns distinct from black holes.
The theoretical challenge is that thin-shell wormholes face severe difficulties. Most solutions are dynamically unstable—perturbations cause them to collapse or expand. The exotic matter requirements are enormous, far exceeding what quantum field theory allows in normal circum stances. No known astrophysical process forms wormholes, unlike black holes which form from stellar collapse.
Nevertheless, thoroughly testing whether astrophysical compact objects might be horizonless alternatives to black holes is scientifically important. General relativity so strongly predicts black holes that finding something else would indicate either a fundamental flaw in our under standing or exotic physics beyond the standard model. The observational tests described above will systematically close loopholes, either confirming black holes or revealing surprises.
Jacobsen: Can information-theoretic diagnostics reveal quantum gravity corrections at current observational sensitivities?
Sakallı: Information theory—the mathematical framework for quantifying information, uncertainty, and correlations—provides a novel lens for exploring quantum gravity. Traditional approaches focus on measuring physical quantities like masses, spins, and frequencies. Information-theoretic approaches ask: how much information do observations carry about the underlying physics? Can we detect quantum gravitational effects through information content rather than direct parameter measurements?
The holographic principle suggests that information in any region of space is bounded by the region’s surface area rather than volume—as if the three-dimensional world is holographically encoded on a two-dimensional boundary. For black holes, this manifests as the Bekenstein Hawking entropy being proportional to horizon area. Quantum corrections modify this rela tionship, adding logarithmic and higher-order terms in the area.
One information-theoretic approach analyzes the entropy of black hole shadows. The shadow pattern observed by telescopes carries information about the spacetime geometry. We can quantify this through Shannon entropy: treating the brightness distribution as a probability distribution and computing its entropy. Quantum corrections alter how photons propagate near the horizon, subtly changing the shadow structure and therefore its information content.
The challenge is scale. For astrophysical black holes, Planck-scale quantum corrections are suppressed by the ratio of the Planck length to the black hole size—roughly 10 to the minus 78th power for a solar-mass black hole. Direct detection of such tiny effects is hopeless with foreseeable technology.
However, indirect signatures might be more accessible. Rather than looking for tiny shifts in individual measurements, we can examine correlations and information flow. For gravitational wave signals, the mutual information between early inspiral and late ringdown phases quantifies how much information from the initial state survives to the final state. Quantum corrections introduce non-Markovian effects—memory effects where the system’s evolution depends on its history rather than just its current state. These memory effects could create measurable corre lation patterns.
Fisher information quantifies how much information data carries about physical parameters. For Event Horizon Telescope observations, we can construct the Fisher information matrix describing precision limits on measuring black hole mass, spin, and potential quantum correction parameters. Current analysis suggests achieving roughly 10 to 30 percent precision on dimensionless quantum parameters—not sufficient to detect Planck-scale effects but potentially constraining if quantum gravity involves larger characteristic scales.
Relative entropy (also called Kullback-Leibler divergence) measures how much observed distributions differ from general relativity predictions. Accumulating this measure across many observations provides a statistical test: are we seeing what general relativity predicts, or are systematic deviations emerging?
Population statistics offer multiplicative power. While individual gravitational wave detections have limited precision, combining information from hundreds or thousands of events (expected in the next decade) increases statistical power. If quantum corrections produce consistent small biases across all events, population-level analysis might reveal them.
Cross-correlation approaches combine complementary observations. Measuring a black hole’s mass from gravitational waves and independently from its shadow size provides a consistency test. If quantum corrections affect these measurements differently, inconsistencies would signal new physics even if neither measurement alone shows deviations.
For primordial black holes—hypothetical small black holes from the early universe—information theoretic signatures might be more accessible. Their much smaller sizes enhance quantum corrections substantially. If primordial black holes exist and their evaporation products are detected, the information content in their emission spectra could constrain quantum gravity.
Realistic assessment requires acknowledging limitations. Directly detecting Planck-scale quan tum gravity through astrophysical observations probably remains beyond reach. However, information-theoretic methods might reveal emergent quantum phenomena accumulating at astrophysical scales, modified information flow during black hole evaporation, or indirect con straints ruling out large classes of quantum gravity theories. These indirect routes may prove more fruitful than searching for minute corrections to individual measurements.
Jacobsen: How do non-extensive entropy formalisms reshape Anti-de Sitter black hole phase diagrams?
Sakallı: Non-extensive statistical mechanics, particularly Tsallis entropy, offers a fascinating general ization of conventional thermodynamics that has profound implications for black hole physics. The standard Boltzmann-Gibbs entropy assumes that systems are extensive—meaning the en tropy of two independent systems simply adds. But for systems with long-range interactions, like gravity, or systems with fractal structure, this additivity breaks down. Tsallis introduced a parameter, typically called q, that quantifies this non-extensivity. When q equals one, we recover standard thermodynamics; deviations from unity signal non-extensive behavior.
For black holes in Anti-de Sitter spacetime—a universe with negative cosmological constant that curves like a saddle rather than a sphere—thermodynamics becomes particularly rich. AdS black holes can undergo phase transitions remarkably similar to everyday substances transitioning between solid, liquid, and gas phases. The famous Hawking-Page transition, where thermal radiation in empty AdS competes with forming a black hole, parallels water freezing into ice.
When we replace standard entropy with Tsallis entropy, the phase diagram transforms dra matically. The temperature-entropy relationship changes because temperature, defined as the derivative of energy with respect to entropy, now involves the non-extensivity parameter. For astrophysical black holes with enormous entropy, even small deviations of q from unity can shift transition temperatures substantially.
The heat capacity—which determines thermodynamic stability—becomes modified in intricate ways. Standard AdS black holes have a critical radius where heat capacity diverges, signaling a phase transition. With Tsallis entropy, this critical point shifts. Depending on whether q exceeds or falls below unity, the transition can occur at smaller or larger radii, or in extreme cases, disappear entirely or split into multiple transitions.
Perhaps most intriguing is the emergence of reentrant phase transitions—phenomena where increasing temperature causes the system to cycle through the same phase multiple times. Imagine heating ice, which melts to water, but continuing to heat causes it to refreeze, then melt again at even higher temperatures. Such behavior, absent in standard thermodynamics, appears naturally when black hole entropy becomes non-extensive. This suggests the underlying quantum gravity degrees of freedom organizing the horizon might have complex, fractal-like structure.
The Hawking-Page transition also shifts under non-extensive statistics. This transition repre sents a competition between entropy favoring thermal radiation spread throughout space and energy minimization favoring localized black holes. With modified entropy, the balance point changes. For q greater than one, transitions occur at lower temperatures; for q less than one, higher temperatures are needed.
Through the AdS/CFT correspondence—the remarkable duality between gravity in AdS space time and quantum field theory on its boundary—modifications to bulk thermodynamics reflect in boundary physics. The confining-deconfining transition in strongly coupled gauge theories, relevant for understanding quark-gluon plasma in heavy-ion collisions, would exhibit modified behavior if the gravitational dual involves non-extensive entropy.
The physical origin of non-extensivity in black holes remains debated. It might arise from quan tum fluctuations of the horizon, long-range gravitational correlations between horizon degrees of freedom, or fractal microstructure of spacetime near the Planck scale. Observationally, con straining the parameter q from astrophysical black holes is extremely challenging, but laboratory analogs using cold atoms or condensed matter systems might provide testable predictions.
Jacobsen: What about the interpretation of Hawking-Page transitions under non-extensive entropy?
Sakallı: The Hawking-Page transition represents one of the most elegant connections between quan tum field theory, gravity, and thermodynamics. In pure AdS spacetime, we can have thermal radiation at some temperature, or we can have a black hole at that temperature. Which con figuration has lower free energy depends on the temperature. At low temperatures, thermal radiation dominates; at high temperatures, black holes are favored. The transition between these phases occurs at a specific critical temperature.
When entropy becomes non-extensive, this picture enriches considerably. The free energy—energy minus temperature times entropy—depends on how entropy scales. With Tsallis entropy, the relationship between physical temperature and thermodynamic temperature becomes modified by a function of the horizon area. This modifies the free energy comparison between phases.
The latent heat—energy exchanged during the phase transition—changes dramatically. For standard black holes, the latent heat reflects the entropy jump when thermal radiation condenses into a black hole. With non-extensive entropy, this jump scales differently with black hole size. For large black holes and q greater than unity, the latent heat can become orders of magnitude larger than in standard thermodynamics, suggesting the transition involves reorganizing vastly more microscopic degrees of freedom.
The order of the transition can even change. Standard Hawking-Page is first-order, with discon tinuous entropy at the transition point, like ice melting to water. But for certain special values of the non-extensivity parameter, the transition can become second-order, with continuous en tropy but divergent heat capacity, like the magnetic transition in iron when heated above its Curie temperature. Between these regimes lie tricritical points where the transition character changes.
Through AdS/CFT, the Hawking-Page transition corresponds to confinement-deconfinement in the boundary gauge theory. At low temperatures, quarks and gluons are confined into hadrons—thermal AdS. At high temperatures, they form quark-gluon plasma—the black hole phase. Non-extensive modifications suggest the strongly coupled plasma might have non standard statistical properties, potentially observable in heavy-ion collisions at RHIC or LHC.
The interpretation becomes particularly interesting when considering the transition’s dynamical aspects. How quickly does thermal radiation condense into a black hole? How long does the mixed phase persist? Non-extensive statistics introduces memory effects—the system’s evolution depends on its history, not just its current state. This non-Markovian character might leave signatures in gravitational wave observations if black holes form dynamically through such transitions in the early universe.
Multiple phase transitions can emerge in extended phase space where we vary not just tem perature but also pressure, charge, and angular momentum. The resulting phase diagrams can exhibit multiple critical points, isolated regions of stability, and complex connectivity between phases—far richer than standard thermodynamics allows.
Discussion
Across its four themes, the excerpt advances a consistent thesis: the most reliable claims in gravitational physics are those formulated in terms of quantities that survive changes of description—ensemble choice, coordinate gauge, or computational representation—without losing physical meaning.
On the KSS bound, Sakallı’s position hinges on separating instantaneous microscopic variability from thermodynamic statements. The bound is treated as an assertion about ensemble-averaged transport and entropy rather than snapshot ratios of fluctuating horizon data. This move is not merely semantic; it aligns the bound with how viscosity and entropy are actually defined in statistical mechanics and hydrodynamics, and it clarifies why fluctuations should not be interpreted as counterexamples. The appeal to causality is also structurally important: in holography, apparent violations are not just “small corrections,” but would imply pathologies (such as superluminal signal propagation) in the dual field theory. The result is a picture in which quantum and higher-derivative effects shift the bound’s numerical value in controlled, model-dependent ways while preserving a lower-bound structure enforced by consistency conditions.
The segment on thermodynamic topology extends this concern for invariance into phase structure. By treating thermodynamic state space as a manifold and critical points as topological defects, the excerpt reframes phase transitions as objects that can be classified by invariants (winding number, topological charge) rather than by coordinate-dependent signatures alone. Ensemble dependence, often a practical nuisance in black-hole thermodynamics, is interpreted geometrically through Legendre transformations on a phase space with ensemble-independent structure. This provides a principled way to say when an invariant is “well-posed”: it must be defined on structures that do not change under reparameterization, and the manifold must be handled globally (including compactification) so that charges and conservation statements are mathematically meaningful.
The unification of linear dilaton, NUT, and Bardeen geometries functions as a case study in how departures from the Kerr–Newman template tend to recur in recognizable families. The shared features—additional hair, generalized asymptotics, modified temperature/entropy relations, and comparable shifts in photon spheres and ISCOs—support an interpretation in which “nonstandard” black holes are not ad hoc curiosities but coordinated outcomes of extended actions and additional fields. The excerpt’s observational remarks underline an important asymmetry: current data often constrain large deviations but still permit moderate hair, making the landscape of alternatives scientifically live rather than purely speculative.
Finally, the comparison of higher-order WKB and neural networks foregrounds a methodological dualism familiar across contemporary physics. WKB is valued for analytic control and interpretability but suffers from convergence and gauge subtleties and demands careful handling of boundary conditions. Neural networks promise speed and broad exploration but import risks that are epistemically different—dependence on training sets, unreliable extrapolation, and limited transparency. Sakallı’s proposed hybrid strategy is therefore not a compromise for its own sake; it is an explicit division of labor between exploration and verification, with physical interpretation and out-of-distribution caution serving as the safeguards that keep fast computation from becoming fast self-deception.
Methods
The interview was conducted via typed questions—with explicit consent—for review, and curation. This process complied with applicable data protection laws, including the California Consumer Privacy Act (CCPA), Canada’s Personal Information Protection and Electronic Documents Act (PIPEDA), and Europe’s General Data Protection Regulation (GDPR), i.e., recordings if any were stored securely, retained only as needed, and deleted upon request, as well in accordance with Federal Trade Commission (FTC) and Advertising Standards Canada guidelines.
Data Availability
No datasets were generated or analyzed during the current article. All interview content remains the intellectual property of the interviewer and interviewee.
References
This interview was conducted as part of a broader quantum cosmology book project. The responses reflect my current research perspective as of October 2025, informed by over 180 publications and ongoing collaborations with researchers worldwide.
Selected References
General Background and Foundational Works
Hawking, S.W. (1974). Black hole explosions? Nature, 248(5443), 30-31. Bekenstein, J.D. (1973). Black holes and entropy. Physical Review D, 7(8), 2333.
Bardeen, J.M., Carter, B., & Hawking, S.W. (1973). The four laws of black hole mechanics. Communications in Mathematical Physics, 31(2), 161-170.
Modified Gravity and Quantum Corrections
Sakallı, ˙I., & Sucu, E. (2025). Quantum tunneling and Aschenbach effect in nonlinear Einstein Power-Yang-Mills AdS black holes. Chinese Physics C, 49, 105101.
Sakallı, ˙I., Sucu, E., & Dengiz, S. (2025). Quantum-Corrected Thermodynamics of Conformal Weyl Gravity Black Holes: GUP Effects and Phase Transitions. arXiv preprint 2508.00203.
Al-Badawi, A., Ahmed, F., & Sakallı, ˙I. (2025). A Black Hole Solution in Kalb-Ramond Gravity with Quintessence Field: From Geodesic Dynamics to Thermal Criticality. arXiv preprint 2508.16693.
Sakallı, ˙I., Sucu, E., & Sert, O. (2025). Quantum-corrected thermodynamics and plasma lensing in non-minimally coupled symmetric teleparallel black holes. Physical Review D, 50, 102063.
Ahmed, F., Al-Badawi, A., & Sakallı, ˙I. (2025). Perturbations and Greybody Factors of AdS Black Holes with a Cloud of Strings Surrounded by Quintessence-like Field in NLED Scenario. arXiv preprint 2510.19862.
Black Hole Thermodynamics and Phase Transitions
Gashti, S.N., Sakallı, ˙I., & Pourhassan, B. (2025). Thermodynamic scalar curvature and topo logical classification in accelerating charged AdS black holes under rainbow gravity. Physics of the Dark Universe, 50, 102136.
Sucu, E., & Sakallı, ˙I. (2025). AdS black holes in Einstein-Kalb-Ramond gravity: Quantum 26 corrections, phase transitions, and orbital dynamics. Nuclear Physics B, 1018, 117081.
Sakallı, ˙I., Sucu, E., & Dengiz, S. (2025). Weak gravity conjecture in ModMax black holes: weak cosmic censorship and photon sphere analysis. European Physics C, 85, 1144.
Pourhassan, B., & Sakallı, ˙I. (2025). Transport phenomena and KSS bound in quantum corrected AdS black holes. European Physics C, 85(4), 369.
Gashti, S.N., Sakallı, ˙I., Pourhassan, B., & Baku, K.J. (2025). Thermodynamic topology, photon spheres, and evidence for weak gravity conjecture in charged black holes with perfect fluid within Rastall theory. Physics Letters B, 869, 139862.
Quasinormal Modes and Spectroscopy
Gashti, S.N., Afshar, M.A., Sakallı, ˙I., & Mazandaran, U. (2025). Weak gravity conjecture in ModMax black holes: weak cosmic censorship and photon sphere analysis. arXiv preprint 2504.11939.
Sakallı, ˙I., & Kanzi, S. (2023). Superradiant (In)stability, Greybody Radiation, and Quasi normal Modes of Rotating Black Holes in Non-Linear Maxwell f(R) Gravity. Symmetry, 15, 873.
Observational Tests and Gravitational Lensing
Sucu, E., & Sakallı, ˙I. (2025). Probing Starobinsky-Bel-Robinson gravity: Gravitational lensing, thermodynamics, and orbital dynamics. Nuclear Physics B, 1018, 116982.
Mangut, M., G¨ursel, H., & Sakallı, ˙I. (2025). Lorentz-symmetry violation in charged black-hole thermodynamics and gravitational lensing: effects of the Kalb-Ramond field. Chinese Physics C, 49, 065106.
Ahmed, F., Al-Badawi, A., & Sakallı, ˙I. (2025). Geodesics Analysis, Perturbations and Deflec tion Angle of Photon Ray in Finslerian Bardeen-Like Black Hole with a GM Surrounded by a Quintessence Field. Annalen der Physik, e2500087.
Generalized Uncertainty Principle and Quantum Effects
Ahmed, F., Al-Badawi, A., & Sakallı, ˙I. (2025). Photon Deflection and Magnification in Kalb Ramond Black Holes with Topological String Configurations. arXiv preprint 2507.22673.
Ahmed, F., & Sakallı, ˙I. (2025). Exploring geodesics, quantum fields and thermodynamics of Schwarzschild-AdS black hole with a global monopole in non-commutative geometry. Nuclear Physics B, 1017, 116951.
Wormholes and Exotic Compact Objects
Ahmed, F., Al-Badawi, A., & Sakallı, ˙I. (2025). Gravitational lensing phenomena of Ellis Bronnikov-Morris-Thorne wormhole with global monopole and cosmic string. Physics Letters B, 864, 139448.
Ahmed, F., & Sakallı, ˙I. (2025). Dunkl black hole with phantom global monopoles: geodesic analysis, thermodynamics and shadow. European Physics C, 85, 660.
Information Theory and Holography
Pourhassan, B., Sakallı, ˙I., et al. (2022). Quantum Thermodynamics of an M2-Corrected Reissner-Nordstr¨om Black Hole. EPL, 144, 29001.
Sakallı, ˙I., & Kanzi, S. (2022). Topical Review: greybody factors and quasinormal modes for black holes in various theories – fingerprints of invisibles. Turkish Journal of Physics, 46, 51-103.
Modified Theories and String Theory
Sakallı, İ., & Yörük, E. (2023). Modified Hawking radiation of Schwarzschild-like black hole in bumblebee gravity model. Physics Scripta, 98, 125307.
Sucu, E., & Sakallı, ˙I. (2023). GUP-reinforced Hawking radiation in rotating linear dilaton black hole spacetime. Physics Scripta, 98, 105201.
Event Horizon Telescope and Observational Cosmology
Event Horizon Telescope Collaboration (2019). First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole. The Astrophysical Journal Letters, 875(1), L1.
Abbott, B.P., et al. (LIGO Scientific Collaboration and Virgo Collaboration) (2016). Observa tion of Gravitational Waves from a Binary Black Hole Merger. Physical Review Letters, 116(6), 061102.
Recent Collaborative Works
Tangphati, T., Sakallı, ˙I., Banerjee, A., & Pradhan, A. (2024). Behaviors of quark stars in the Rainbow Gravity framework. Physical Review D, 46, 101610.
Banerjee, A., Sakallı, ˙I., Pradhan, A., & Dixit, A. (2024). Properties of interacting quark star in light of Rastall gravity. Classical and Quantum Gravity, 42, 025008.
Sakallı, ˙I., Banerjee, A., Dayanandan, B., & Pradhan, A. (2025). Quark stars in f(R, T) gravity: mass-to-radius profiles and observational data. Chinese Physics C, 49, 015102.
Gashti, S.N., Sakallı, ˙I., Pourhassan, B., & Baku, K.J. (2024). Thermodynamic topology and phase space analysis of AdS black holes through non-extensive entropy perspectives. European Physics C, 85, 305.
Al-Badawi, A., & Sakallı, ˙I. (2025). The Static Charged Black Holes with Weyl Corrections. International Journal of Theoretical Physics, 64, 50.
Textbooks and Reviews
Carroll, S.M. (2004). Spacetime and Geometry: An Introduction to General Relativity. Addison Wesley.
Wald, R.M. (1984). General Relativity. University of Chicago Press.
Rovelli, C. (2004). Quantum Gravity. Cambridge University Press.
Kiefer, C. (2012). Quantum Gravity (3rd ed.). Oxford University Press. Ashtekar, A., & Petkov, V. (Eds.) (2014). Springer Handbook of Spacetime. Springer.
Note: This reference list includes representative works from Prof. Sakallı’s extensive publication record (181+ papers) and foundational works in the field. For a complete bibliography, please consult the INSPIRE-HEP database or Prof. Sakallı’s institutional profile.
Journal & Article Details
Publisher: In-Sight Publishing
Publisher Founding: March 1, 2014
Web Domain: http://www.in-sightpublishing.com
Location: Fort Langley, Township of Langley, British Columbia, Canada
Journal: In-Sight: Interviews
Journal Founding: August 2, 2012
Frequency: Four Times Per Year
Review Status: Non-Peer-Reviewed
Access: Electronic/Digital & Open Access
Fees: None (Free)
Volume Numbering: 14
Issue Numbering: 1
Section: A
Theme Type: Discipline
Theme Premise: Quantum Cosmology
Formal Sub-Theme: None.
Individual Publication Date: February 22, 2026
Issue Publication Date: April 1, 2026
Author(s): Scott Douglas Jacobsen
Word Count: 3,278
Image Credits: Izzet Sakallı
ISSN (International Standard Serial Number): 2369-6885
Acknowledgements
The author acknowledges Tor Arne Jørgensen for her time, expertise, and valuable contributions. Her thoughtful insights and detailed explanations have greatly enhanced the quality and depth of this work, providing a solid foundation for the discussion presented herein.
Author Contributions
S.D.J. conceived the subject matter, conducted the interview, transcribed and edited the conversation, and prepared the manuscript.
Competing Interests
The author declares no competing interests.
License & Copyright
In-Sight Publishing by Scott Douglas Jacobsen is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
© Scott Douglas Jacobsen and In-Sight Publishing 2012–Present.
Unauthorized use or duplication of material without express permission from Scott Douglas Jacobsen is strictly prohibited. Excerpts and links must use full credit to Scott Douglas Jacobsen and In-Sight Publishing with direction to the original content.
Supplementary Information
Below are various citation formats for Causality, Ensemble Invariance, and Black-Hole Perturbations: Prof. Dr. ˙Izzet Sakallı on the KSS Bound, Thermodynamic Topology, and Quasinormal-Mode Inference (3) (Scott Douglas Jacobsen, February 22, 2026).
American Medical Association (AMA 11th Edition)
Jacobsen SD. Causality, Ensemble Invariance, and Black-Hole Perturbations: Prof. Dr. ˙Izzet Sakallı on the KSS Bound, Thermodynamic Topology, and Quasinormal-Mode Inference (3). In-Sight: Interviews. 2026;14(1). Published February 22, 2026. http://www.in-sightpublishing.com/causality-ensemble-invariance-black-hole-perturbations-izzet-sakalli-kss-bound-thermodynamic-topology-quasinormal-mode-inference
American Psychological Association (APA 7th Edition)
Jacobsen, S. D. (2026, February 22). Causality, ensemble invariance, and black-hole perturbations: Prof. Dr. ˙Izzet Sakallı on the KSS bound, thermodynamic topology, and quasinormal-mode inference (3). In-Sight: Interviews, 14(1). In-Sight Publishing. http://www.in-sightpublishing.com/causality-ensemble-invariance-black-hole-perturbations-izzet-sakalli-kss-bound-thermodynamic-topology-quasinormal-mode-inference
Brazilian National Standards (ABNT)
JACOBSEN, Scott Douglas. Causality, Ensemble Invariance, and Black-Hole Perturbations: Prof. Dr. ˙Izzet Sakallı on the KSS Bound, Thermodynamic Topology, and Quasinormal-Mode Inference (3). In-Sight: Interviews, Fort Langley, v. 14, n. 1, 22 fev. 2026. Disponível em: http://www.in-sightpublishing.com/causality-ensemble-invariance-black-hole-perturbations-izzet-sakalli-kss-bound-thermodynamic-topology-quasinormal-mode-inference
Chicago/Turabian, Author-Date (17th Edition)
Jacobsen, Scott Douglas. 2026. “Causality, Ensemble Invariance, and Black-Hole Perturbations: Prof. Dr. ˙Izzet Sakallı on the KSS Bound, Thermodynamic Topology, and Quasinormal-Mode Inference (3).” In-Sight: Interviews 14 (1). http://www.in-sightpublishing.com/causality-ensemble-invariance-black-hole-perturbations-izzet-sakalli-kss-bound-thermodynamic-topology-quasinormal-mode-inference.
Chicago/Turabian, Notes & Bibliography (17th Edition)
Jacobsen, Scott Douglas. “Causality, Ensemble Invariance, and Black-Hole Perturbations: Prof. Dr. ˙Izzet Sakallı on the KSS Bound, Thermodynamic Topology, and Quasinormal-Mode Inference (3).” In-Sight: Interviews 14, no. 1 (February 22, 2026). http://www.in-sightpublishing.com/causality-ensemble-invariance-black-hole-perturbations-izzet-sakalli-kss-bound-thermodynamic-topology-quasinormal-mode-inference.
Harvard
Jacobsen, S.D. (2026) ‘Causality, Ensemble Invariance, and Black-Hole Perturbations: Prof. Dr. ˙Izzet Sakallı on the KSS Bound, Thermodynamic Topology, and Quasinormal-Mode Inference (3)’, In-Sight: Interviews, 14(1), 22 February. Available at: http://www.in-sightpublishing.com/causality-ensemble-invariance-black-hole-perturbations-izzet-sakalli-kss-bound-thermodynamic-topology-quasinormal-mode-inference.
Harvard (Australian)
Jacobsen, SD 2026, ‘Causality, Ensemble Invariance, and Black-Hole Perturbations: Prof. Dr. ˙Izzet Sakallı on the KSS Bound, Thermodynamic Topology, and Quasinormal-Mode Inference (3)’, In-Sight: Interviews, vol. 14, no. 1, 22 February, viewed 22 February 2026, http://www.in-sightpublishing.com/causality-ensemble-invariance-black-hole-perturbations-izzet-sakalli-kss-bound-thermodynamic-topology-quasinormal-mode-inference.
Modern Language Association (MLA, 9th Edition)
Jacobsen, Scott Douglas. “Causality, Ensemble Invariance, and Black-Hole Perturbations: Prof. Dr. ˙Izzet Sakallı on the KSS Bound, Thermodynamic Topology, and Quasinormal-Mode Inference (3).” In-Sight: Interviews, vol. 14, no. 1, 2026, http://www.in-sightpublishing.com/causality-ensemble-invariance-black-hole-perturbations-izzet-sakalli-kss-bound-thermodynamic-topology-quasinormal-mode-inference.
Vancouver/ICMJE
Jacobsen SD. Causality, Ensemble Invariance, and Black-Hole Perturbations: Prof. Dr. ˙Izzet Sakallı on the KSS Bound, Thermodynamic Topology, and Quasinormal-Mode Inference (3) [Internet]. 2026 Feb 22;14(1). Available from: http://www.in-sightpublishing.com/causality-ensemble-invariance-black-hole-perturbations-izzet-sakalli-kss-bound-thermodynamic-topology-quasinormal-mode-inference
Note on Formatting
This document follows an adapted Nature research-article format tailored for an interview. Traditional sections such as Methods, Results, and Discussion are replaced with clearly defined parts: Abstract, Keywords, Introduction, Main Text (Interview), and a concluding Discussion, along with supplementary sections detailing Data Availability, References, and Author Contributions. This structure maintains scholarly rigor while effectively accommodating narrative content.
In-Sight Publishing 