arXiv subjects

Chandrasekhar Bhamidipati

Publications and source records attributed to Chandrasekhar Bhamidipati.

At least 19 recordsLinked to original sources

arXiv2026

Criticality of ISCOs and AdS/CFT

We study the trajectories of massive particles in spherically symmetric black holes in arbitrary dimensions, and find certain universal features based on the topological classification of the fixed points. If the system admits a center, we find two possible outcomes: regardless of the value of the angular momentum, the center always survives, which is realized in global AdS spacetimes or, the center disappears below a critical value of angular momentum, which happens for various spherically symmetric black holes. For the latter case, we find that irrespective of the details of the black hole, there must always be a saddle point. Topological arguments show that there exists a certain critical value of energy, angular momentum and the angular velocity, where the center and the saddle coalesce. This happens at a special point in the parameter space where the trajectories are the limiting innermost stable circular orbits (ISCOs). At the critical point, conserved quantities show universal, van der Waals-like mean-field scaling typical of a second-order phase transition. The anomalous dimensions $γ$ of the double-twist operators in the CFT are found, both using AdS/CFT and through the the heavy-heavy-light-light four point correlators, giving negative and positive values for the center and saddle, respectively, including the emergence of certain non-analytic behaviour at the ISCO. For the center, we also find subleading corrections in $\frac{1}{Δ_H}$ to $γ$ in the dual CFT, and dsicuss the implications of our results.

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arXiv2026

Off-shell Thermodynamics and Kinetics of Holographic CFTs Dual to Charged AdS Black Holes

We study the thermodynamics and phase structure of holographic conformal field theories dual to spherically symmetric charged AdS black holes using an off-shell free energy. We consider three ensembles of the dual CFT with fixed: $(\tilde Q,{\cal V},C)$, $(\tilde Φ,{\cal V},C)$, and $(\tilde Q,{\cal V},μ)$ and present their corresponding phase diagrams. For the fixed $(\tilde Q,{\cal V},C)$ and $(\tilde Φ,{\cal V},C)$ ensembles, we study the transitions between competing states using a stochastic description on the various phases given by off-shell free energy. This is described by an ensemble dependent Fokker-Planck equation, allowing us to compute the first-passage-time distribution, including the mean first passage time and its fluctuations over a range of temperatures. We also examine how the phase structure and the associated kinetics depend on the electric charge $\tilde Q$ and the central charge $C$.

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arXiv2026

ISCOs and the weak gravity conjecture bound in higher derivative theories of gravity

We study circular orbits of charged particles in spherically symmetric AdS black holes in higher derivative theories of gravity, and their limiting ISCOs (innermost stable circular orbits). The dual interpretation is in terms of heavy-light double twist conformal field theory (CFT) operators in the large spin limit, whose anomalous dimensions can be extracted from the binding energy of charged probes in the bulk, in a certain large orbit limit. Demanding the positivity of the anomalous dimensions, leads to an exact bound for the charge to mass ratio $\hat q$ of probe particles in the black hole backgrounds, which matches with the WGC bound. We find that $\hat q$ increases with the higher derivative coupling parameters, which is explicitly checked in the Gauss-Bonnet gravity. For existing computations with probe particles in AdS backgrounds, the anomalous dimension and the WGC bound we find, particularly in Gauss-Bonnet theories, are in agreement in appropriate limits with the recent computations for Schwarzschild AdS arXiv:2009.04500, charged AdS arXiv:2305.08907 and neutral Gauss-Bonnet black holes in AdS arXiv:2204.09749. Finally, we show that the ISCOs exist until the limit set by the WGC bound, with their radius decreasing with coupling parameters, which we check explicitly for the case of Gauss-Bonnet black holes in AdS.

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arXiv2026

Topological charge and black hole photon spheres in massive gravity

In this paper, we investigate the existence and nature of the photon spheres (PS) in the background of four dimensional static and spherically symmetric black holes in the de Rham-Gabadadze-Tolley (dRGT) massive gravity theory. Apart from the known case of one PS, there are regions in the parameter space of massive gravity where either two or no PS's exist outside the event horizon. Topological arguments show that, the case of one PS falls in the category of Einstein gravity (with topological charge $-1$), whereas, the cases with two or zero PS's belong to a different topological class with total charge zero. PS's of horizonless compact objects, also belong to the same class with total topological charge $0$, though, one distinction can be made with the black holes in massive gravity. While in the former case, the inner PS is stable, in the later case, it is the outer PS which is stable (the inner PS is unstable). We also study the landscape of possible regions of existence of standard and exotic photon spheres in the massive gravity parameter space, and correlate it with the horizon structure of the black holes.

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arXiv2026

Off-shell phase diagram of BPS black holes in AdS$_5$

We construct the off-shell free energy of supersymmetric black holes in AdS$_5$, and study the phase diagram in various limiting cases, with particular emphasis on BPS thermodynamics. The changes to the free energy following from the four-derivative corrections to five-dimensional minimal gauged supergravity action are computed, and the modifications to the phase diagram are studied. Starting from Landau's theory, an exact method is systematically developed to construct the off shell BPS free energy, which in certain limiting cases, can be rearranged in terms of an effective energy and entropy of the system, with the later being conjugate to an effective BPS temperature. The off-shell BPS phase diagram shows features which resemble the phases of general AdS Schwarzschild black holes, with some nuances in the asymptotic structure, modified by four-derivative corrections. Using AdS/CFT, phenomenological effective potentials in the boundary gauge theory are proposed, dual to both general black holes and their BPS counterparts. The saddle points of the effective potential capture the various locally stable and unstable phases of the gauge theory at finite temperature and chemical potential.

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arXiv2025

Static spheres and Aschenbach effect for black holes in massive gravity

In this paper, we study the trajectories of massive and massless particles in four dimensional static and spherically symmetric black holes in de Rham-Gabadadze-Tolley (dRGT) massive gravity theory via phase-plane analysis and point out several novel features. In particular, we show the existence of a static sphere, a finite radial distance outside the black holes in these theories, where a massive particle can be at rest, as seen by an asymptotic zero angular momentum observer. Topological arguments show that the stable and unstable static spheres, which come in pairs, have opposite charges. In the presence of angular momentum, we first study the behaviour of massless particles and find the presence of stable and unstable photon spheres in both neutral and charged black holes. Subsequently, we study the motion of massive test particles around these black holes, and find one pair of stable and unstable time-like circular orbits (TCOs), such that the stable and unstable TCO's are disconnected in certain regions. Computing the angular velocity $Ω_{\text{\tiny CO}}$ of the TCOs, measured by a static observer at rest, shows the unusual nature of its monotonic increase with the radius of TCO, near the location of stable photon sphere. This confirms the existence of Aschenbach effect for spherically symmetric black holes in massive gravity, which was only found to exist in rapidly spinning black holes, with the only other exception being the rare example of gravity coupled to quasi-topological electromagnetism.

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arXiv2024

Topology of critical points in boundary matrix duals

Computation of topological charges of the Schwarzschild and charged black holes in AdS in canonical and grand canonical ensembles allows for a classification of the phase transition points via the Bragg-Williams off-shell free energy. We attempt a topological classification of the critical points and the equilibrium phases of the dual gauge theory via a phenomenological matrix model, which captures the features of the ${\cal{N}}=4$, $SU(N)$ Super Yang-Mills theory on $S^3$ at finite temperature at large $N$. With minimal modification of parameters, critical points of the matrix model at finite chemical potential can be classified as well. The topological charges of locally stable and unstable dynamical phases of the system turn out to be opposite to each other, totalling to zero, and this matches the analysis in the bulk.

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arXiv2023

Cardy-Verlinde formula from boundary matrix model

Cardy-Verlinde (CV) formula relates the entropy of a conformal field theory (CFT) in arbitrary dimensions to its total energy (with an appropriate insertion of additional internal energy for charged systems) and Casimir energy. While several aspects of the CV formula have been tested directly for weakly coupled CFTs, the aim of the present paper is to verify it in the strongly coupled regime, by employing a phenomenological matrix model, which captures the features of the ${\cal{N}}=4$, $SU(N)$ Super Yang-Mills theory on $S^3$ at finite temperature and chemical potential at large $N$.

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arXiv2023

Topology of Hawking-Page transition in Born-Infeld AdS black holes

Black holes in anti de Sitter (AdS) spacetimes undergo phase transitions which typically lead to the existence of critical points, that can be classified using topological techniques. Availing the Bragg-Williams construction which provides an off-shell free energy formalism, we compute the topological charge of the Hawking-Page (HP) transition for Einstein-Born-Infeld black holes in anti de Sitter spacetime and match the result with the confinement-deconfinement transition in the dual gauge theory, which turn out to be in perfect agreement.

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arXiv2023

Thermodynamic curvature of charged black holes with $AdS_2$ horizons

Sign and magnitude of the thermodynamic curvature provides empirical information about the nature of microstructures of a general thermodynamic system. For charged black holes in AdS, thermodynamic curvature is positive for large charge or chemical potential, and diverges for extremal black holes, indicating strongly repulsive nature. We compute the thermodynamic curvature at low temperatures, for charged black holes with AdS$_2$ near horizon geometry, and containing a zero temperature horizon radius $r_h$, in a spacetime which asymptotically approaches $AdS_D$ (for $D>3$). In the semi-classical analysis at low temperatures, the curvature shows a novel crossover from negative to positive side, indicating the shift from attraction to repulsion dominated regime near $T=0$, before diverging as $1/(γT)$, where $γ$ is the coefficient of leading low temperature correction to entropy. Accounting for quantum fluctuations, the curvature computed in the canonical ensemble is positive, whereas the one in the grand canonical ensemble, continues to show a crossover from negative to positive side. Moreover, the divergence of curvature at $T=0$ is cured irrespective of the ensemble used, resulting in a universal constant.

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arXiv2023

Contact and metric structures in black hole chemistry

We review recent studies of contact and thermodynamic geometry for black holes in AdS spacetimes in the extended thermodynamics framework. The cosmological constant gives rise to the notion of pressure $P = -Λ/ 8 π$ and, subsequently a conjugate volume $V$, thereby leading to a close analogy with hydrostatic thermodynamic systems. To begin with, we review the contact geometry approach to thermodynamics in general and then consider thermodynamic metrics constructed as the Hessians of various thermodynamic potentials. We then study their correspondence to statistical ensembles for systems with two-dimensional spaces of equilibrium states. From the zeroes and divergences of the curvature scalar obtained from the metric, we carefully analyze the issue of ensemble non-equivalence and show certain complimentary behaviors in the description of a thermodynamic system. Following a thorough analysis of the familiar van der Waals system, we turn our attention to black holes in extended phase space. Considering the example of charged AdS black holes, we discuss the generic features of their thermodynamic geometry in detail. The relationship of the thermodynamic curvature(s) with critical points as well as microscopic interactions in black holes is also briefly explored. We finally set up the thermodynamic geometry for finite temperature gauge theories dual to black holes in AdS via holographic correspondence and comment on recent progress.

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arXiv2022

Topology of Born-Infeld AdS black holes in 4D novel Einstein-Gauss-Bonnet gravity

The topological classification of critical points of black holes in 4D Einstein-Gauss-Bonnet gravity coupled to Born-Infeld theory is investigated. Considered independently, Born-infeld corrections to the Einstein action alter the topological charge of critical points of the charged AdS black hole system, whereas the Gauss-Bonnet corrections do not. For the combined system though, the total topological charge of the Einstein-Gauss-Bonnet theory is unaltered in the presence of Born-Infeld coupling.

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arXiv2022

Novel logarithmic corrections to black hole entropy

For a thermodynamic system, apart from thermal fluctuations, there are also fluctuations in thermodynamic volume when the system is in contact with a volume reservoir. For the case of black holes in anti-de Sitter spacetimes, the effect of thermal fluctuations on the entropy is well studied. The aim of this work is to compute novel logarithmic corrections to black hole entropy coming from simultaneous fluctuations of energy and thermodynamic volume. We work in the isothermal-isobaric ensemble and first obtain a general form of corrections to entropy which are valid for any thermodynamic system. Applying the formalism to Kerr black holes in AdS reveals that the black hole entropy gets corrected as: $\mathcal{S} = S_0 - k \ln S_0 + \cdots$ where $S_0$ is given by the Bekenstein-Hawking formula and $k = - 1$. The same leading coefficient is also obtained in the canonical ensemble, i.e. by considering energy fluctuations alone. This coefficient is found to be unaltered in the slowly rotating and high temperature limits.

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arXiv2022

Topology of critical points and Hawking-Page transition

Using the Bragg-Williams construction of an off-shell free energy we compute the topological charge of the Hawking-Page transition point for black holes in AdS. A computation following from a related off-shell effective potential in the boundary gauge dual matches the value of topological charge obtained in the bulk. We also compute the topological charges of the equilibrium phases of these systems, which follow from the saddle points of the appropriate free energy. The locally stable and unstable phases turn out to have topological charges opposite to each other, with the total being zero, in agreement with the result obtained from a related construction [arXiv:2208.01932].

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arXiv2022

Logarithmic corrections to the entropy function of black holes in the open ensemble

An `open' or $(μ,P,T)$-ensemble describes equilibrium systems whose control parameters are chemical potential $μ$, pressure $P$ and temperature $T$. Such an unconstrained ensemble is seldom used for applications to standard thermodynamic systems due to the fact that the corresponding free energy identically vanishes as a result of the Euler relation. However, an open ensemble is perfectly regular for the case of black holes, as the entropy is a quasi-homogeneous function of extensive thermodynamic variables with scaling dictated by the Smarr formula. Following a brief discussion on thermodynamics in the open ensemble, we compute the general form of logarithmic corrections to the entropy of a typical system, due to fluctuations in energy, thermodynamic volume and a generic charge $N$. This is then used to obtain the exact analytic form of the logarithmically corrected black hole entropy for charged and rotating black holes in anti-de Sitter spacetimes.

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arXiv2022

Logarithmic corrections to black hole entropy and holography

We compute logarithmic corrections to the black hole entropy $S_{\rm bh}$ in a holographic set up where the cosmological constant $Λ$ and Newton's constant $G_D$ are taken to be thermodynamic parameters, related to variations in bulk pressure $P$ and central charge $c$. In the bulk, the logarithmic corrections are of the form: $\mathcal{S} = S_{\rm bh} - k \ln S_{\rm bh} + \cdots$ arising due to fluctuations in thermodynamic volume, induced by a variable $Λ$, in addition to energy fluctuations. We explicitly compute this coefficient $k$ for the BTZ black hole and show that the result matches with the one coming from the logarithmic corrections to the Cardy's formula. We propose an entropy function in the CFT, which exactly reproduces the logarithmic corrections to black hole entropy in arbitrary dimensions.

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arXiv2022

Topology of black hole thermodynamics in Gauss-Bonnet gravity

Thermodynamics of black holes in anti de Sitter (AdS) spacetimes typically contains critical points in the phase diagram, some of which correspond to the first order transition ending in a second order one. Following the recent proposal in [arXiv:2112.01706] on using Duan's $ϕ$-mapping theory, we classify the critical points of six dimensional charged Gauss-Bonnet black holes in AdS spacetime. We find that the higher derivative corrections from Gauss-Bonnet gravity do not change the topological class of critical points in charged black holes in AdS, unlike the case of Born-Infeld corrections noted earlier. The connection between the topological nature of critical points and existence of first order phase transitions breaks down in a certain parameter regime. A resolution is proposed by treating the novel and conventional critical points as phase creation and phase annihilation points, respectively. Examples are provided to support the proposal.

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arXiv2021

A note on size-momentum correspondence and chaos

The aim of this note is to explore Susskind's proposal [arXiv:1802.01198] on the connection between operator size in chaotic theories and the bulk momentum of a particle falling into black holes (see also [arXiv:1804.04156, 1806.05574, 1904.12819, 1912.05996, 2006.03019] for more recent generalizations), in a broad class of models involving Gauss-Bonnet(GB) and Lifshitz-Hyperscaling violating theories in AdS. For Gauss-Bonnet black holes, the operator size is seen to be suppressed as the coupling constant $λ$ is increased. For the Lifshitz-hyperscaling violating theories characterised by the parameters $z$ and $θ$, the operator size is higher as compared to case $z=1,θ=0$ (Reissner-Nordstrom AdS black holes). In the case of operators with global charge corresponding to charged particles falling into black holes, suppression of chaos is seen in general theories of gravity, in conformity with the original proposal [arXiv:1802.01198] and earlier findings [arXiv:1806.05574].

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