arXiv subjects

Ankit Anand

Publications and source records attributed to Ankit Anand.

At least 19 recordsLinked to original sources

arXiv2026

Crossover from Schwarzian dynamics to rotational soft modes in near-extremal Lovelock black holes

Near-extremal black holes are controlled by a small set of soft modes, and counting these modes fixes the coefficient of $\log T$ in the entropy. We ask whether genuine six-derivative interactions change that count, working in seven-dimensional third-order Lovelock gravity, the simplest setting where the cubic Lovelock term is dynamical. The multiplicities stay the same, but the naive count fails. At fixed charge the Maxwell mode is frozen out, and the fifteen rotational modes of the $S^5$ act as a quantum rotor that only switches on above the scale $K_J^{-1}$. As a result, the coefficient of $\log T$ runs from $3/2$ at the lowest temperatures to $9$ above that scale, and never reaches the naive Gaussian value $19/2$. We compute the moment of inertia $K_J$ from the charged slow-rotation solution and find that the Lovelock couplings move the crossover without changing the multiplicities. Only large AdS black holes have a wide window in which the full rotational contribution competes with the classical entropy. Adding a probe charged scalar, we derive an analytic near-horizon Schwinger threshold in the cubic coupling. Its large-AdS limit tells us when the broad rotational crossover window can coexist with the absence of a charged-scalar Breitenlohner--Freedman (BF) bound violation.

hep-th↗

arXiv2026

Saddle-Order Universality in Ensemble-Averaged Black Hole Thermodynamics

We establish a saddle-order proposition for the ensemble-averaged generalized free energy in reduced Euclidean black hole ensembles. Under regularity and stability assumptions, the leading fluctuation contribution is determined by the order of the first stabilizing term around the dominant saddle. An ordinary critical point is governed by a quartic soft mode, giving a quarter-temperature contribution instead of the familiar half-temperature Gaussian result. We verify this analytically for four-dimensional RN-AdS and Kerr-AdS black holes and map their thermodynamic controls to a common quartic normal form, whose scaling function connects the critical and Gaussian regimes along the zero-field one-well direction. The proposition also extends to coupled collective modes with weighted-homogeneous leading potentials. These results provide a unified description of reduced-ensemble fluctuations through black hole criticality.

hep-th↗

arXiv2026

Using Reward Uncertainty to Induce Diverse Behaviour in Reinforcement Learning

Classical reinforcement learning (RL) typically seeks a deterministic policy that maximizes the expected sum of a scalar reward. Yet, modern applications such as language model fine-tuning or scientific discovery demand diversity. Existing remedies such as entropy regularization or diversity bonuses often require fragile trade-offs that sacrifice performance for stochasticity or rely on heuristic metrics that can misalign policy rankings. We argue that diversity is more naturally understood as the rational response to uncertainty in the reward. When the reward function is not perfectly known--as is the case with ambiguous preferences or imperfect reward models--committing to a single action can be sub-optimal. Building on this, we propose a fundamental reformulation of the RL objective by replacing the scalar reward with a distribution over reward functions, and applying a non-linear objective over sets of actions. The result is a framework in which calibrated behavioural diversity emerges naturally, remains controllable through the reward function distribution, and is obtained without sacrificing expected reward. Focusing on the contextual bandit setting as commonly used in large language model (LLM) post-training, we derive a principled gradient estimator for this objective and prove that our formulation naturally generalizes both vanilla policy gradient and more recently developed action-set approaches. We provide didactic experiments which complement our theoretical results, and our large-scale empirical results in LLM reasoning further demonstrate that this framework offers a robust and theoretically grounded alternative for complex RL tasks where the traditional formulation of the problem fails to induce the desired breadth of agent behaviour.

cs.LG↗

arXiv2026

Reconstructing $f(R)$ gravity from generalized entropies: exact Lagrangians

Generalized horizon entropies are widely used as theoretical modifications of the Bekenstein-Hawking area law, but through the Wald construction they may also encode modifications of the underlying gravitational dynamics. We reconstruct metric $f(R)$ gravity from prescribed entropy-area relations and show that the procedure is intrinsically branch dependent through the required area-curvature map. On the maximally symmetric branch, where $A=48π/R$ exactly, the reconstruction reduces to a single quadrature and can be performed non-perturbatively. We obtain closed-form Lagrangians for several generalized entropies and show that an entropy term $a~S_{BH}^{q}$ generates a curvature term proportional to $R^{2-q}$. In particular, Kaniadakis entropy produces a $1/R$ correction, while logarithmic entropy generates an $R^2\ln R$ term. We further derive a branch-independent criterion, $\partial_{R}^{2} f=(ds/dR)d(S/s)/ds$, relating Dolgov-Kawasaki stability directly to the entropy functional, together with $m_{\rm sc}^2=S'(s)/(3f_{RR})$ on the maximally symmetric branch. Comparison with the fixed-mass Schwarzschild-de Sitter branch reveals different reconstructed Lagrangians and reversed stability properties. Finally, the weak-isolated-horizon boost charge reproduces the original generalized entropy. These results establish a direct non-perturbative link between generalized horizon thermodynamics and modified gravitational dynamics.

gr-qc↗

arXiv2026

From arithmetic spectra to a quantum-corrected black hole geometry

The Euler product of the Riemann zeta function is the partition function of a free bosonic gas whose mode energies are the logarithms of the primes. We show that this arithmetic gas, combined with the assumption that the entropy--geometry correspondence holds, leads to a quantum-corrected black-hole metric. The prime gas is a Hagedorn system. Its entropy is linear in the energy, which is exactly what an entropy linear in the horizon area requires, and the simple pole of the zeta function at $β=1$ fixes the coefficient of the logarithmic correction to the area law. The nontrivial zeros cannot play this role: their level density grows only logarithmically, and far too slowly to be extensive. Demanding that the reconstructed geometry reduce to Schwarzschild at large radius then fixes the map from arithmetic energy to horizon area and yields the closed-form metric $f(r)=1-2GMr/(r^{2}+\lz^{2})$ with $\lz^{2}=αG/π$. This describes a two-horizon black hole with Reissner--Nordström horizon structure but no Coulombic hair, a positive-energy anisotropic source obeying the null energy condition, a softened central singularity, a bounded Hawking temperature, and a cold extremal remnant that ends the evaporation. The same length scale follows independently from requiring that the first law hold exactly with the corrected entropy. The nontrivial zeros survive only as exponentially suppressed log-periodic ripples in the area, which suggests a physical interpretation of the Riemann hypothesis as the statement that arithmetic corrections to black-hole thermodynamics are as small as they can be.

gr-qc↗

arXiv2026

Entanglement islands and information recovery from near-extremal regular black holes

We investigate the Page curve and information recovery in a near-extremal regular black hole inspired by T-duality, in which the central singularity is resolved by a minimal length scale. By integrating the first law of thermodynamics at fixed minimal length, we obtain a black-hole entropy containing an intrinsically quantum logarithmic correction, while the area-law contribution vanishes in the extremal limit. Consequently, the extremal remnant carries a finite entropy of purely quantum origin. Using the island prescription in the near-horizon regime, we evaluate the generalized entropy of radiation and compare the standard area functional with an alternative functional constructed from the corrected thermodynamic entropy of the black hole. In the near-extremal limit, the latter reduces analytically to the classical extremization problem with an effective coupling, and it places the physical island closer to the outer horizon. Although both prescriptions produce a Page transition, they predict different saturation values and Page times. While the standard functional yields a plateau controlled by the area term, the corrected prescription saturates at the full thermodynamic entropy of the outer horizon and, in the extremal limit, at the logarithmic remnant entropy. Including evaporation and backreaction, the Page curve develops the expected descending branch and asymptotes to the entropy of the cold extremal remnant rather than to zero. Our results indicate that a thermodynamically consistent description of information recovery from regular near-extremal black holes requires incorporating the intrinsic quantum correction to the gravitational entropy.

hep-th↗

arXiv2026

Entropy-geometry correspondence as effective nonlocal gravity

We develop an operator formulation of the entropy-geometry correspondence for static, spherically symmetric gravity. Starting from a generalized entropy, we reconstruct an effective nonlocal form factor, its coordinate-space source, the associated cumulative mass profile, and the resulting spacetime geometry. The construction is worked out for the Bekenstein-Hawking, Rényi, Tsallis-Cirto, Barrow, Kaniadakis entropies, logarithmically/exponentially corrected entropy and LQG inspired entropy. The operator representation provides a direct relation between generalized entropy, nonlocal gravitational dressing, and a scale-dependent effective mass or Newton coupling. We analyze the reconstructed sources and their infrared and ultraviolet behavior, discuss their physical consistency, and identify the limits in which the standard Schwarzschild description is recovered. We show that the generalized entropy exactly reproduces the area law with the reconstructed running Newton coupling, $\dd S=\dd A/4G_S(r_+)$, ensuring thermodynamic consistency. Since horizon entropy is determined by the action, this favors entropy corrections in the gravitational sector. We also derive the conditions for the reconstructed horizon to be an event horizon with positive temperature.

gr-qc↗

arXiv2026

Noncommutative black holes: Topological bulk-boundary correspondence and Binary Merger Bounds

We investigate the thermodynamic topology of charged AdS black holes in a non-commutative spacetime sourced by Lorentzian-smeared matter distributions. Since exact analytical solutions for the critical thermodynamic quantities are not available, we employ a perturbative expansion in the non-commutative parameter and validate the resulting expressions through numerical analysis. Using the generalized off-shell free-energy framework, we explore the topological structure of the thermodynamic phase space and evaluate the corresponding winding number that characterizes the phase transitions. Our results reveal that non-commutative effects introduce qualitative modifications to the thermodynamic behavior compared with the standard Reissner-Nordström AdS black hole. Furthermore, we demonstrate that the bulk and boundary descriptions possess an identical global thermodynamic topology, providing strong evidence for the correspondence between their topological structures. We also investigate the lower bound on the remnant mass implied by the second law of black-hole thermodynamics and observe that non-commutative corrections modify key thermodynamic quantities, with particular emphasis on the entropy and the final black-hole mass.

gr-qc↗

arXiv2026

Perturbative study of Supercritical Crossover in Noncommutative-corrected Spacetime

We analytically study the Widom line and supercritical crossover of noncommutative charged AdS black holes. Treating the noncommutative parameter $α$ perturbatively, we compute thermodynamic quantities and the scaled variance $Ω$ in both canonical and extended ensembles. The Widom line is identified as the extremum of $Ω$. Using a Landau expansion near the critical point, we derive the two symmetric crossover branches $L^{\pm}$, which obey $δT\sim \left|ΔQ\right|^{β+γ}$, $δS\sim \left|ΔQ \right|^β$ in the canonical ensemble and $δP\sim \left|ΔT\right|^{β+γ}$, $δρ\sim \left|ΔT\right|^β$ in the extended ensemble. These scaling relations conform to the mean-field universality class ($β=1/2$, $γ=1$), and the noncommutative parameter only shifts subleading amplitudes without altering the universality class. Numerical verification and complete supercritical phase diagrams are also presented using supercritical crossover lines. Our results show that noncommutative corrections preserve the mean-field universality of black hole supercriticality.

hep-th↗

arXiv2026

Effective matter sectors from modified entropies

We present a general formalism linking modified entropy functions directly to a modified spacetime metric and, subsequently, to an effective matter sector of entropic origin. In particular, within the framework of general relativity, starting from the first law of black-hole thermodynamics we establish an explicit correspondence between the entropy derivative and the metric function, which naturally leads to an emergent stress-energy tensor representing an anisotropic effective fluid. This backreaction effect of horizon entropy may resolve possible inconsistencies recently identified in black hole physics with modified entropies. As specific examples, we apply this procedure to a wide class of modified entropies, such as Barrow, Tsallis-Cirto, Renyi, Kaniadakis, logarithmic, power-law, loop-quantum-gravity, and exponential modifications, and we derive the associated effective matter sectors, analyzing their physical properties and energy conditions.

gr-qc↗

arXiv2026

Universal Supercritical Behavior in Global Monopole-Charged AdS Black Holes

We analytically investigate the Widom line and universal supercritical crossover for charged AdS black holes threaded by a global monopole. We compute thermodynamic variables in both the extended and canonical ensembles. We derive the scaled variance $Ω$ using the Gibbs free energy and locate the Widom line as the extrema of this. Using mean-field expansion of the equation of state near criticality, we obtain closed-form expressions for the Widom line and the two branching crossover lines $L^\pm$. We show that the monopole parameter shifts the critical parameters but does not change the mean-field universal scaling: the leading linear term and the nonanalytic correction remain universal in both ensembles. We also numerically verify this using the supercritical crossover lines $L^\pm$ and show the universal scaling laws and the complete supercritical phase diagrams.

hep-th↗

arXiv2026

Kerr-de Sitter Black Holes: Quantum Aspects and Cosmic Censorship Conjecture

In this article, we test the validity of the weak cosmic censorship conjecture (wCCC) in the background of a quantum Kerr-de Sitter (qKdS) black hole, incorporating exact backreaction from quantum matter fields. Using a test particle approach, we analyze whether an extremal qKdS black hole can be over-extremized to expose a naked singularity. Our results indicate that the black hole remains stable against horizon-destroying processes induced by infalling matter. Quantum corrections enhance the horizon's robustness rather than destabilize it, offering further evidence that wCCC remains preserved in the presence of quantum effects.

hep-th↗

arXiv2026

Zero-point length as a topological protection of black hole regularity

We investigate the thermodynamic topology of regular black holes with zero-point length using an extended first law that includes the zero-point length stored in the geometry. By treating the regularization scale $l_0$ as a thermodynamic variable, we analyze the Hessian geometry of the thermodynamic manifold and demonstrate that the vector field $\vecϕ = (T, Ψ)$, where $T$ is the temperature and $Ψ$ is the conjugate to $l_0$, never vanishes in the physical parameter space for $l_0 > 0$. This implies the absence of Morse critical points and a vanishing winding number ($W = 0$), indicating topological protection against the formation of naked singularities. Crucially, we show that in the singular limit $l_0 \to 0$, a non-zero winding number ($W = 1$) emerges, characterizing the Schwarzschild singularity as a topological defect. The conservation of this topological invariant under smooth evolution provides a rigorous topological formulation of the weak cosmic censorship conjecture: the presence of zero-point length not only regularizes the spacetime background but also enforces topological protection against the formation of singularities, preventing black hole-to-naked singularity transitions.

gr-qc↗

arXiv2026

Testing the Weak Gravity Conjecture via Gravitational Lensing, Black Hole Shadows, and Barrow Thermodynamics in F(R)-Euler-Heisenberg (A)dS Black Holes

We investigate the interplay of the Weak Gravity Conjecture (WGC) and the Weak Cosmic Censorship Conjecture (WCCC) in $F(R)$-Euler-Heisenberg black holes in Anti-de Sitter and de Sitter backgrounds. The solution is characterized by the electric charge $q$, the $F(R)$ deviation $f_{R_0}$, the Euler--Heisenberg coupling $λ$, and the constant scalar curvature $R_0$. We establish a universal entropy--extremality relation that provides thermodynamic evidence for the WGC independently of $f_{R_0}$ and $R_0$. Photon sphere analysis from both geodesic and topological perspectives confirms the simultaneous compatibility of the WGC and WCCC, with the Euler--Heisenberg coupling restoring photon spheres in the naked singularity regime. Gravitational lensing in the strong- and weak-deflection limits reveals that the photon sphere radius is independent of the cosmological background while the critical impact parameter nearly doubles in de Sitter. Black hole shadow images under isotropic accretion are constructed. Within the Barrow entropy framework, we uncover van der Waals-type phase transitions and analyze Joule-Thomson expansion, identifying the small black hole phase as the WGC-compatible thermodynamic regime accessible via isenthalpic cooling.

gr-qc↗

arXiv2026

The Art of Being Difficult: Combining Human and AI Strengths to Find Adversarial Instances for Heuristics

We demonstrate the power of human-LLM collaboration in tackling open problems in theoretical computer science. Focusing on combinatorial optimization, we refine outputs from the FunSearch algorithm [Romera-Paredes et al., Nature 2023] to derive state-of-the-art lower bounds for standard heuristics. Specifically, we target the generation of adversarial instances where these heuristics perform poorly. By iterating on FunSearch's outputs, we identify improved constructions for hierarchical $k$-median clustering, bin packing, the knapsack problem, and a generalization of Lovász's gasoline problem - some of these have not seen much improvement for over a decade, despite intermittent attention. These results illustrate how expert oversight can effectively extrapolate algorithmic insights from LLM-based evolutionary methods to break long-standing barriers. Our findings demonstrate that while LLMs provide critical initial patterns, human expertise is essential for transforming these patterns into mathematically rigorous and insightful constructions. This work highlights that LLMs are a strong collaborative tool in mathematics and computer science research.

cs.LG↗

arXiv2025

Topological and optical signatures of modified black-hole entropies

We investigate how deviations from the Bekenstein-Hawking entropy modify black-hole spacetimes through the recently proposed entropy-geometry correspondence. For four representative modified entropies, namely Barrow, Rényi, Kaniadakis, and logarithmic, we derive the corresponding effective metrics and analyze their thermodynamic and topological classification using the off-shell free energy and winding numbers. We show that Barrow and Rényi entropies yield a single unstable sector with global charge $W=-1$, while logarithmic and Kaniadakis corrections produce canceling defects with $W=0$, revealing topological structures absent in the Schwarzschild case. Using the modified metrics, we further calculate the photon-sphere radius and shadow size, showing that each modified entropy relation induces characteristic optical shifts. Thus, by comparing with Event Horizon Telescope observations of Sgr A$^\ast$, we extract new bounds on all entropy-deformation parameters. Our results demonstrate that thermodynamic topology, together with photon-sphere phenomenology, offers a viable way to test generalized entropy frameworks and probe departures from the Bekenstein-Hawking area law.

gr-qc↗

arXiv2025

Holographic Entanglement Entropy in Janus deformed AdS$_3$ Geometries

We investigate the time dependent entanglement entropy for boosted single intervals in interface conformal field theories (ICFT$_2$s) dual to Janus deformed AdS$_3$ geometries. For a Janus deformed Poincaré AdS$_3$ background, we obtain the entanglement entropy and a Janus induced correction using a replica technique for the equivalent dual field theory described on a conformally flat background on corresponding AdS$_2$ slices on the asymptotic boundary. The holographic entanglement entropy is then computed through certain embedding relations for the bulk Janus deformed AdS$_3$ geometry which exactly match with the field theory results. We further extend our analysis to investigate the entanglement entropy of corresponding intervals in ICFT$_2$s dual to bulk Janus deformed BTZ black hole and AdS$_3$ black string geometries obtaining consistent results from both the field theoretic and bulk computations.

hep-th↗

arXiv2025

Towards Responsible Development of Generative AI for Education: An Evaluation-Driven Approach

A major challenge facing the world is the provision of equitable and universal access to quality education. Recent advances in generative AI (gen AI) have created excitement about the potential of new technologies to offer a personal tutor for every learner and a teaching assistant for every teacher. The full extent of this dream, however, has not yet materialised. We argue that this is primarily due to the difficulties with verbalising pedagogical intuitions into gen AI prompts and the lack of good evaluation practices, reinforced by the challenges in defining excellent pedagogy. Here we present our work collaborating with learners and educators to translate high level principles from learning science into a pragmatic set of seven diverse educational benchmarks, spanning quantitative, qualitative, automatic and human evaluations; and to develop a new set of fine-tuning datasets to improve the pedagogical capabilities of Gemini, introducing LearnLM-Tutor. Our evaluations show that LearnLM-Tutor is consistently preferred over a prompt tuned Gemini by educators and learners on a number of pedagogical dimensions. We hope that this work can serve as a first step towards developing a comprehensive educational evaluation framework, and that this can enable rapid progress within the AI and EdTech communities towards maximising the positive impact of gen AI in education.

cs.CY↗