Thermodynamics of R-charged Black Holes inAdS5×S5from Effective Strings

The Kerr/CFT correspondence is a possible route to gain insight into the quantum theory of gravity in the near-horizon region of a Kerr black hole via a dual holographic conformal field theory (CFT). Predictions of the black hole entropy, scattering cross-section and the quasi normal modes from the dual holographic CFT corroborate this proposed correspondence. More recently, it has been suggested that quantum gravitational effects in the near-horizon region of a black hole may drastically modify the classical general relativistic description, leading to potential observable consequences. In this paper, we study the absorption cross-section and quasi normal modes of a horizonless Kerr-like exotic compact object (ECO) in the dual CFT picture. Our analysis suggests that the near-horizon quantum modifications of the black hole can be understood as finite size and/or finite $N$ effects in the dual CFT. Signature of the near-horizon modification to a black hole geometry manifests itself as delayed echoes in the ringdown (i.e. the postmerger phase) of a binary black hole coalescence. From our dual CFT analysis we show how the length of the circle, on which the dual CFT lives, must be related to the echo time-delay that depends on the position of the near-horizon quantum structure. We further derive the reflectivity of the ECO membrane in terms of the CFT modular parameters, showing that it takes the Boltzmann form.

We consider a five-dimensional constant curvature black hole, which is constructed by identifying some points along a Killing vector in a five-dimensional AdS space. The black hole has the topology M4×S1, its exterior is time-dependent and its boundary metric is of the form of a three-dimensional de Sitter space times a circle, which means that the dual conformal field theory resides on a dynamical spacetime. We calculate the quasilocal stress-energy tensor of the gravitational background and then the stress-energy tenor of the dual conformal field theory. It is found that the trace of the tensor does indeed vanish, as expected. Further we find that the constant curvature black hole spacetime is just the “bubble of nothing” resulting from Schwarzschild-AdS black holes when the mass parameter of the latter vanishes.

We present a first-principles derivation of the main results of the Kerr/CFT correspondence and its extensions using only tools from gravity and quantum field theory. Firstly, we review properties of extremal black holes with in particular the construction of an asymptotic Virasoro symmetry in the near-horizon limit. The entropy of extremal spinning or charged black holes is shown to match with a chiral half of Cardy’s formula. Secondly, we show how a thermal 2-dimensional conformal field theory (CFT) is relevant to reproduce the dynamics of near-superradiant probes around near-extremal black holes in the semi-classical limit. Thirdly, we review the hidden conformal symmetries of asymptotically-flat black holes away from extremality and present how the non-extremal entropy can be matched with Cardy’s formula. We follow an effective field theory approach and consider the Kerr–Newman black hole and its generalizations in various supergravity theories. The interpretation of these results by deformed dual conformal field theories is discussed and contrasted with properties of standard 2-dimensional CFTs. We conclude with a list of open problems.

We present a first-principles derivation of the main results of the Kerr/CFT correspondence and its extensions using only tools from gravity and quantum field theory, filling a few gaps in the literature when necessary. Firstly, we review properties of extremal black holes that imply, according to semi-classical quantization rules, that their near-horizon quantum states form a centrally-extended representation of the one-dimensional conformal group. This motivates the conjecture that the extremal Kerr and Reissner-Nordström black holes are dual to the chiral limit of a two-dimensional CFT. We also motivate the existence of an SL(2, ℤ) family of two-dimensional CFTs, which describe in their chiral limit the extremal Kerr-Newman black hole. We present generalizations in anti-de Sitter spacetime and discuss other matter-coupling and higher-derivative corrections. Secondly, we show how a near-chiral limit of these CFTs reproduces the dynamics of near-superradiant probes around near-extremal black holes in the semi-classical limit. Thirdly, we review how the hidden conformal symmetries of asymptotically-flat black holes away from extremality, combined with their properties at extremality, allow for a microscopic accounting of the entropy of non-extremal asymptotically-flat rotating or charged black holes. We conclude with a list of open problems.

Holographic superconductors in the AdS black-hole spacetime with a global monopole

In a recent publication we studied the decay rate of primordial black holes perceiving the dark dimension, an innovative five-dimensional (5D) scenario that has a compact space with characteristic length scale in the micron range. We demonstrated that the rate of Hawking radiation of 5D black holes slows down compared to 4D black holes of the same mass. Armed with our findings we showed that for a species scale of O(1010 GeV), an all-dark-matter interpretation in terms of primordial black holes should be feasible for black hole masses in the range 1014≲M/g≲1021. As a natural outgrowth of our recent study, herein we calculate the Hawking evaporation of near-extremal 5D black holes. Using generic entropy arguments we demonstrate that Hawking evaporation of higher-dimensional near-extremal black holes proceeds at a slower rate than the corresponding Schwarzschild black holes of the same mass. Assisted by this result we show that if there were 5D primordial near-extremal black holes in nature, then a primordial black hole all-dark-matter interpretation would be possible in the mass range 105β≲M/g≲1021, where β is a parameter that controls the difference between mass and charge of the associated near-extremal black hole. Published by the American Physical Society 2024

In this paper, we investigate the minimal length effects on the thermodynamics and weak cosmic censorship conjecture in a RN-AdS black hole via charged particle absorption. We first use the generalized uncertainty principle (GUP) to investigate the minimal length effect on the Hamilton-Jacobi equation. After the deformed Hamilton-Jacobi equation is derived, we use it to study the variations of the thermodynamic quantities of a RN-Ads black hole via absorbing a charged particle. Furthermore, we check the second law of thermodynamics and the weak cosmic censorship conjecture in two phase spaces. In the normal phase space, the second law of thermodynamics and the weak cosmic censorship conjecture are satisfied in the usual and GUP-deformed cases, and the minimal length effect makes the increase of entropy faster than the usual case. After the charge particle absorption, the extremal RN-AdS black hole becomes nonextremal. In the extended phase space, the black hole entropy can either increase or decrease. When T>2Pr+, the second law is satisfied. When T<2Pr+, the second law of thermodynamics is violated for the extremal or near-extremal black hole. Finally, we find that the weak cosmic censorship conjecture is legal for extremal and near-extremal RN-Ads black holes in the GUP-deformed case.

We consider asymptotically Warped AdS$_3$ black holes in Topologically Massive Gravity. We study their thermodynamic stability and show the existence of a Hawking-Page phase transition between the black hole and thermal background phases. At zero angular potential, the latter is shown to occur at the self-dual point of the dual Warped Conformal Field Theory partition function, in analogy with the phase transition for BTZ black holes in AdS$_3$/CFT$_2$. We also discuss how the central and vacuum charges can be obtained from inner horizon mechanics in the presence of a gravitational anomaly.

Freudenthal duality (F-duality), an anti-involution of charge vectors, keeps the entropy and attractor solutions invariant for an extremal supersymmetric black hole. We analyze the effect of F-duality on the entropy of a near-extremal STU black hole in $\mathcal{N}=2$ ungauged, four-dimensional supergravity. We consider double-extremal black holes, whose attractor solutions are fixed in terms of the black hole charges throughout the moduli space. It is well known that Jackiw-Teitelboim (JT) gravity governs the dynamics of the near-horizon regions of higher-dimensional, near-extremal black holes. Owing to this fact, we reduce the four-dimensional supergravity theory to two dimensions to construct a JT gravity--like model and compute the near-extremal entropy. We then analyze the effect of F-duality on this entropy. We show that the F-duality breaks down for the case of near-extremal solutions if one considers the duality operation generated through near-extremal entropy rather than the extremal one.

The thermodynamics and weak cosmic censorship conjecture in Reissner-Nordström anti-de Sitter black holes are investigated by the scattering of the scalar field. The first law of thermodynamics in the non-extremal Reissner-Nordström anti-de Sitter black hole is recovered by the scattering. The increase of the horizon radius indicates that the singularity is not naked in this black hole. For the near-extremal and extremal black holes, the validity is tested by the minimum values of the function f at their final states. It is found that both of the near-extremal and extremal black holes can not be overcharged. When ω=qϕ, the final state of the extremal black hole is still an extremal black hole. When ω≠qϕ, it becomes a near-extremal black hole with new mass and charge.

We construct the microstates of near-extremal black holes in AdS_5 x S5 as gases of defects distributed in heavy BPS operators in the dual SU(N) Yang-Mills theory. These defects describe open strings on spherical D3-branes in the S5, and we show that they dominate the entropy by directly enumerating them and comparing the results with a partition sum calculation. We display new decoupling limits in which the field theory of the lightest open strings on the D-branes becomes dual to a near-horizon region of the black hole geometry. In the single-charge black hole we find evidence for an infrared duality between SU(N) Yang-Mills theories that exchanges the rank of the gauge group with an R-charge. In the two-charge case (where pairs of branes intersect on a line), the decoupled geometry includes an AdS_3 factor with a two-dimensional CFT dual. The degeneracy in this CFT accounts for the black hole entropy. In the three-charge case (where triples of branes intersect at a point), the decoupled geometry contains an AdS_2 factor. Below a certain critical mass, the two-charge system displays solutions with naked timelike singularities even though they do not violate a BPS bound. We suggest a string theoretic resolution of these singularities.

The superconformal index of N = 4 supersymmetric Yang-Mills theory with gauge group U(N) has provided powerful insights into the entropy of supersymmetric black holes in AdS5× S5, including some sub-leading logarithmic and non-perturbative corrections. Recently, the phase space of supersymmetric solutions has been argued to contain configurations other than the asymptotically AdS5 black hole. Such configurations include the so-called grey galaxies where the black hole at the center is surrounded by a gas of gravitons. By numerically evaluating the superconformal index of N = 4 supersymmetric Yang-Mills at small values of N, we detect systematic deviations from the entropy of black holes with two distinct angular momenta. We find that the giant graviton expansion of the index is a numerically efficient way of evaluating the index that complements the direct character evaluation and allows for explicit access to N ≤ 15 with up to two giant gravitons in the expansion. We find it remarkable that a supersymmetric quantity in field theory, usually thought of as a rigid counting observable, indeed contains information about different phases in the space of supersymmetric solutions on the gravity side.

We construct a series of new hyperbolic black hole solutions in Einstein–Scalar system and we apply holographic approach to investigate the spherical Rényi entropy in various deformations of dual conformal field theories (CFTs). Especially, we introduce various powers of scalars in the scalar potentials for massive and massless scalar. These scalar potentials correspond to deformation of dual CFTs. Then we solve asymptotically hyperbolic AdS black hole solutions numerically. We map the instabilities of these black hole solutions to phase transitions of field theory in terms of CHM mapping between hyperbolic hairy AdS black hole and spherical Rényi entropy in dual field theories. Based on these solutions, we study the temperature dependent condensation of dual operator of massive and massless scalar respectively. These condensations show that there might exist phase transitions in dual deformed CFTs. We also compare free energy between asymptotically hyperbolic AdS black hole solutions and hyperbolic AdS Schwarz (AdS-SW) black hole to test phase transitions. In order to confirm the existence of phase transitions, we turn on linear in-homogeneous perturbation to test stability of these hyperbolic hairy AdS black holes. In this paper, we show how potential parameters affect the stability of hyperbolic black holes in several specific examples. For general values of potential parameters, it needs further study to see how the transition happens. Finally, we comment on these instabilities associated with spherical Rényi entropy in dual deformed CFTs.

We study the decay of a near-extremal black hole in AdS$_2$, related to the near-horizon region of 3+1-dimensional Reissner-Nordstr\\"om spacetime, following Fabbri, Navarro, and Navarro-Salas. Back-reaction is included in a semiclassical approximation. Calculations of the stress-energy tensor of matter coupled to the physical spacetime for an affine null observer demonstrate that the black hole evaporation proceeds smoothly and the near-extremal black hole evolves back to an extremal ground state, until this approximation breaks down.

The weak cosmic censorship conjecture in the near-extremal BTZ black hole has been tested using test particles and fields. It has been claimed that such a black hole can be overspun. In this paper, we review the thermodynamics and weak cosmic censorship conjecture in BTZ black holes using the scattering of a scalar field. The first law of thermodynamics in the non-extremal BTZ black hole is recovered. For the extremal and near-extremal black holes, due to the divergence of the variation of entropy, we test the weak cosmic censorship conjecture by evaluating the minimum of the function f, and find that both the extremal and near-extremal black holes cannot be overspun.