2D Black Hole Research Articles

Analytic long-lived modes in charged critical plasma

Fluctuations around critical behavior of a holographic charged plasma are investigated by studying quasi-normal modes of the corresponding black branes in 5D Einstein-Maxwell-Dilaton gravity. The near horizon geometry of black branes approaches the well-known 2D charged string black hole in the critical limit, for which a world-sheet description is available, and the corresponding quasi-normal modes can be obtained analytically from the reflection amplitude of the 2D black hole geometry. We find two distinct set of modes: a purely imaginary “decoupled” set, directly following from the reflection amplitude, and a “non-decoupled” set that was already identified in the neutral holographic plasma in [1]. In the extremal limit, the former set of imaginary quasi-normal modes coalesce on a branch cut starting from the origin, signaling breakdown of hydrodynamic approximation. We further complete the black brane geometry with a slice of AdS near the boundary, to allow for a holographic construction, and find another set of modes localized in the UV. Finally, we develop an alternative WKB method to obtain the quasi-normal modes in the critical limit and apply this method to study the spectrum of hyperscaling-violating Lifshitz black branes. The critical limit of the plasma we consider in this paper is in one-to-one correspondence with the large D limit of Einstein’s gravity which allows for an alternative interesting interpretation of our findings.

M2-branes on discs and multi-charged spindles

We study supersymmetric AdS2 × Y9 solutions of 11d supergravity where Y9 is an S7 fibration over a Riemann surface equipped with a metric of non-constant curvature. We consider two classes of Riemann surface: the first is a spindle and the second is a topological disc. These solutions are interpreted as the near-horizon limit of M2 branes wrapped on the Riemann surface and describe the near-horizon of a 4d black hole. In the case of the topological disc there are additional flavour M2 branes smeared on a five-sphere embedded in the transverse S7. We perform a full global analysis of both classes of solutions, both from a 4d and an 11d viewpoint. Finally we compute the two-dimensional Newton’s constant from which we obtain a prediction for the entropy of the black hole.

Five dimensional rotating regular black holes and shadow

Higher-dimensional theories admit that astrophysical objects like supermassive black holes are somewhat different from standard ones and that their optical properties deviate from general relativity. A black hole casts a shadow as an optical appearance because of its strong gravitational field, and a black hole shadow could be used to determine which theory of gravity is consistent with observations. Measurements of the shadow sizes around the black holes can help evaluate various parameters of the black hole metric and may provide an opportunity to find signatures of extra dimensions. We present an exact five-dimensional (5D) rotating regular black hole metric, with a deviation parameter \(k\ge 0\), that interpolates between the 5D Kerr black hole (\(k=0\)) and 5D Kerr–Newman (\(r \gg k\)). This 5D rotating regular black hole is an exact general relativity solution coupled to nonlinear electrodynamics. Interestingly, for a given value of parameter k, there exits a critical angular momentum \(a=a_E\), which corresponds to an extremal rotating regular black hole with degenerate horizons. At the same time, for \(a<a_E\), one has a non-extremal rotating regular black hole with outer and inner horizons. Owing to the correction factor (\(e^{-k/r^2}\)), which is motivated by the quantum arguments, the ergoregion and shadow of 5D black holes are modified.

Central charges for AdS black holes

Nontrivial diffeomorphisms act on the horizon of a generic 4D black holes and create distinguishing features referred to as soft hair. Amongst these are a left–right pair of Virasoro algebras with associated charges that reproduce the Bekenstein–Hawking entropy for Kerr black holes. In this paper we show that if one adds a negative cosmological constant, there is a similar set of infinitesimal diffeomorphisms that act non-trivially on the horizon. The algebra of these diffeomorphisms gives rise to a central charge. Adding a boundary counterterm, justified to achieve integrability, leads to well-defined central charges with c L = c R. The macroscopic area law for Kerr-AdS black holes follows from the assumption of a Cardy formula governing the black hole microstates.

Eliminating Black Holes Singularity in Brane World Cosmology

In recent works, a construction was proposed resulting in emergent universes inside black holes. This result can be obtained from a 4D black hole embedded in a 5D spacetime with the fifth dimension compactified on a circle [0, 2] (0 and 2 are identified) such that the two branes are at 0 and 1. In the present work, we study this setup by deriving particles’ equations of motion in the new universes, based on redefining energy and angular momentum. This leads to disappearance of the singularity in centers of black holes in classical General Relativity.

Quasi-normal modes and microscopic description of 2D black holes

We investigate the possibility of using quasi-normal modes (QNMs) to probe the microscopic structure of two-dimensional (2D) anti-de Sitter (AdS2) dilatonic black holes. We first extend previous results on the QNMs spectrum, found for external massless scalar perturbations, to the case of massive scalar perturbations. We find that the quasi-normal frequencies are purely imaginary and scale linearly with the overtone number. Motivated by this and extending previous results regarding Schwarzschild black holes, we propose a microscopic description of the 2D black hole in terms of a coherent state of N massless particles quantized on a circle, with occupation numbers sharply peaked on the characteristic QNMs frequency hat{omega} . We further model the black hole as a statistical ensemble of N decoupled quantum oscillators of frequency hat{omega} . This allows us to recover the Bekenstein-Hawking (BH) entropy S of the hole as the leading contribution to the Gibbs entropy for the set of oscillators, in the high-temperature regime, and to show that S = N. Additionally, we find sub-leading logarithmic corrections to the BH entropy. We further corroborate this microscopic description by outlining a holographic correspondence between QNMs in the AdS2 bulk and the de Alfaro-Fubini-Furlan conformally invariant quantum mechanics. Our results strongly suggest that modelling a black hole as a coherent state of particles and as a statistical ensemble of decoupled harmonic oscillators is always a good approximation in the large black-hole mass, large overtone number limit.

Rotating 5D black holes: Interactions and deformations near extremality

We study a two-dimensional theory of gravity coupled to matter that is relevant to describe holographic properties of black holes with two equal angular momenta in five dimensions (with or without cosmological constant). We focus on the near-horizon geometry of the near-extremal black hole, where the effective theory reduces to Jackiw-Teitelboim (JT) gravity coupled to a massive scalar field. We compute the corrections to correlation functions due to cubic interactions present in this theory. A novel feature is that these corrections do not have a definite sign: for AdS_55 black holes the sign depends on the mass of the extremal solution. We discuss possible interpretations of these corrections from a gravitational and holographic perspective. We also quantify the imprint of the JT sector on the UV region, i.e. how these degrees of freedom, characteristic for the near-horizon region, influence the asymptotically far region of the black hole. This gives an interesting insight on how to interpret the IR modes in the context of their UV completion, which depends on the environment that contains the black hole.

P − V criticality and Joule-Thomson expansion of Hayward-AdS black holes in 4D Einstein-Gauss-Bonnet gravity

In this paper, the P−V criticality and Joule-Thomson Expansion of Hayward-AdS black holes in 4D Einstein-Gauss-Bonnet gravity are studied in the extended phase space. We find the black hole always exhibits a phase transition similar to that of the Van der Waals system for any arbitrary positive parameters α and g. We also study the dependence of α and g on the inversion curves and plot the inversion and isenthalpic curves in the T−P plane, which can determine the cooling-heating regions.

From the BTZ black hole to JT gravity: geometrizing the island

We study the evaporation of two-dimensional black holes in JT gravity from a three-dimensional point of view. A partial dimensional reduction of AdS3 in Poincaré coordinates leads to an extremal 2D black hole in JT gravity coupled to a ‘bath’: the holographic dual of the remainder of the 3D spacetime. Partially reducing the BTZ black hole gives us the finite temperature version. We compute the entropy of the radiation using geodesics in the three-dimensional spacetime. We then focus on the finite temperature case and describe the dynamics by introducing time-dependence into the parameter controlling the reduction. The energy of the black hole decreases linearly as we slowly move the dividing line between black hole and bath. Through a re-scaling of the BTZ parameters we map this to the more canonical picture of exponential evaporation. Finally, studying the entropy of the radiation over time leads to a geometric representation of the Page curve. The appearance of the island region is explained in a natural and intuitive fashion.

Holographic JT gravity with quartic couplings

We construct the most general theory of 2D Einstein-dilaton gravity coupled with U(1) gauge fields that contains all the 2-derivative and the 4-derivative interactions allowed by the diffeomorphism invariance. We renormalise the 2D action and obtain the vacuum solution as well as the black hole solution. The vacuum solution in the UV is dominated by Lifshitz2 with dynamical exponent (z = frac{7}{3} ) while on the other hand, the spacetime curvature diverges as we move towards the deep IR limit. We calculate the holographic stress tensor and the central charge for the boundary theory. Our analysis shows that the central charge goes as the inverse power of the coupling associated to 4-derivative interactions. We also compute the Wald entropy for 2D black holes and interpret its near horizon divergence in terms of the density of states. We compare the Wald entropy with the Cardy formula and obtain the eigen value of Virasoro operator (L0) for our model. Finally, we explore the near horizon structure of 2D black holes and calculate the central charge corresponding to the CFT near horizon. We further show that the near horizon CFT may be recast as a 2D Liouville theory with higher derivative corrections. We study the Weyl invariance of this generalised Liouville theory and identify the Weyl anomaly associated to it. We also comment on the classical vacuum structure of the theory.

Islands with gravitating baths: towards ER = EPR

We study the Page curve and the island rule for black holes evaporating into gravitating baths, with an eye towards establishing a connection with the ER=EPR proposal. We consider several models of two entangled 2d black holes in Jackiw-Teitelboim (JT) gravity with negative cosmological constant. The first, “doubled PSSY,” model is one in which the black holes have end-of-the-world (ETW) branes with a flavour degree of freedom. We study highly entangled states of this flavour degree of freedom and find an entanglement-induced Hawking-Page-like transition from a geometry with two disconnected black holes to one with a pair of black holes connected by a wormhole, thus realising the ER = EPR proposal. The second model is a dynamical one in which the ETW branes do not have internal degrees of freedom but the JT gravity is coupled to a 2d CFT, and we entangle the black holes by coupling the two CFTs at the AdS boundary and evolving for a long time. We study the entanglement entropy between the two black holes and find that the story is substantially similar to that with a non-gravitating thermal bath. In the third model, we couple the two ends of a two-sided eternal black hole and evolve for a long time. Finally, we discuss the possibility of a Hawking-Page-like transition induced by real-time evolution that realises the ER = EPR proposal in this dynamical setting.

The topologically twisted index of mathcal{N} = 4 SU(N) Super-Yang-Mills theory and a black hole Farey tail

We investigate the large-N asymptotics of the topologically twisted index of mathcal{N} = 4 SU(N) Super-Yang-Mills (SYM) theory on T2 × S2 and provide its holographic interpretation based on the black hole Farey tail [1]. In the field theory side, we use the Bethe-Ansatz (BA) formula, which gives the twisted index of mathcal{N} = 4 SYM theory as a discrete sum over Bethe vacua, to compute the large-N asymptotics of the twisted index. In a dual mathcal{N} = 2 gauged STU model, we construct a family of 5d extremal solutions uplifted from the 3d black hole Farey tail, and compute the regularized on-shell actions. The gravitational partition function given in terms of these regularized on-shell actions is then compared with a canonical partition function derived from the twisted index by the inverse Laplace transform, in the large-N limit. This extends the previous microstate counting of an AdS5 black string by the twisted index and thereby improves holographic understanding of the twisted index.

AdS/BCFT correspondence and BTZ black hole thermodynamics within Horndeski gravity

In this work, we study gravity duals of conformal field theories with boundaries known as AdS/BCFT correspondence, put forward by Takayanagi [1], within a scalar-tensor theory, as proposed by Horndeski in 4D [2]. We consider the case of 3D gravity dual to 2D BCFT, take a Gibbons-Hawking surface term modified by Horndeski's theory and find the corresponding 3D (BTZ) black hole solutions. We analyze the effects of Horndeski's gravity on the profile of the extra boundary for the black hole by using an approximate analytic solution. Performing a holographic renormalization, we have calculated the free energy and obtained the total entropy and the corresponding area, as well as the boundary entropy for the black hole. In particular, the boundary entropy found here, can be seen as an extension of the one proposed by Takayanagi. From the free energy, we have done a systematic study of the 3D black hole thermodynamics and present, among our results, an indication of restoration of conformal symmetry for high temperatures. Finally, we present a study on the influence of the Horndeski's gravity on the Hawking-Page phase transition where we can see the stable and unstable phases throughout the plane of free energy {\sl versus} temperature.

Shadow cast and quasinormal modes in f(R) gravity model inspired by Yang–Mills field

In this paper, the null geodesic equations are computed in [Formula: see text] space–time dimensions [Y. Younesizadeh, A. A. Ahmad, A. H. Ahmed, F. Younesizadeh, Ann. Phys. 420, 168246 (2020)] by using the concept of symmetries and Hamilton–Jacobi equation and Carter separable method. With these null geodesics in hand, we evaluate the celestial coordinates (x, y) and the radius [Formula: see text] of the BH shadow and represent it graphically. In addition, we have shown that the peak of this energy slowly shifts to lower frequencies and its height decreases with the increase in the YM magnetic charge ([Formula: see text]) values and decrease in the [Formula: see text] parameter ([Formula: see text]) values. In addition, we have analyzed the concept of effective potential barrier by transforming the radial equation of motion into standard Schrodinger form. The most important result derived from this study is that the height of this potential increases with increase in the YM magnetic charge ([Formula: see text]) values. Then, we study the quasinormal modes (QNMs) of these 4D black holes. For this purpose, we use the WKB approximation method upto third-order corrections. We have shown the perturbation’s decay in corresponding diagrams when the YM magnetic charge ([Formula: see text]) values and the [Formula: see text] parameter ([Formula: see text]) values change.

Fuzzy and discrete black hole models* *The first author was partially supported by CONACyT (México).

Using quantum Riemannian geometry, we solve for a Ricci = 0 static spherically-symmetric solution in 4D, with the S 2 at each t, r a noncommutative fuzzy sphere, finding a dimension jump with solutions having the time and radial form of a classical 5D Tangherlini black hole. Thus, even a small amount of angular noncommutativity leads to radically different radial behaviour, modifying the Laplacian and the weak gravity limit. We likewise provide a version of a 3D black hole with the S 1 at each t, r now a discrete circle , with the time and radial form of the inside of a classical 4D Schwarzschild black hole far from the horizon. We study the Laplacian and the classical limit . We also study the 3D FLRW model on with S 2 an expanding fuzzy sphere and find that the Friedmann equation for the expansion is the classical 4D one for a closed Universe.

Charged black hole solutions with Toroidal horizons in f(R)-gravity surrounded by quintessence and cloud of strings: Effective potential barrier, quasinormal modes

We construct a new class of [Formula: see text]-dimensional black hole solutions with Toroidal horizons in [Formula: see text] gravity framework which is surrounded by quintessence and string cloud configuration, whose asymptotic structures are determined by the quintessential state parameter [Formula: see text] and dimension’s parameter [Formula: see text]. We point out that the asymptotic behavior of the obtained solutions is neither asymptotically flat nor (A)dS when we have [Formula: see text] and [Formula: see text]. Regarding the cosmological constant as a thermodynamic pressure and its conjugate quantity as a thermodynamic volume, we investigate the critical behavior of our black hole solutions. In [Formula: see text] and [Formula: see text], the P–V diagrams are more complex than that of the standard Van der Waals. These diagrams behave like the Born–Infeld-AdS P–V diagrams. When [Formula: see text] and [Formula: see text], the P–V diagrams behave like the standard Van der Waals system (In this work [S. Gunasekaran, D. Kubiznaak and R. B. Mann, Extended phase space thermodynamics for charged and rotating black holes and Born–Infeld vacuum polarization, J. High Energy Phys. (2012).] [S. Gunasekaran, D. Kubiznaak and R.B. Mann, Extended phase space thermodynamics for charged and rotating black holes and Born–Infeld vacuum polarization, J. High Energy Phys. (2012)], the authors believe that the BTZ black holes, contrary to the higher-dimensional case, do not show any critical behavior. In this work, we have showed that the three-dimensional (3D) black holes can also have critical behavior and coincide with those of the Van der Waals system). Besides, we have analyzed the concept of effective potential barrier by transforming the radial equation of motion into standard Schrodinger form. We figure out the effect of the coupling constant [Formula: see text], the string parameter b, and the quintessential state parameter [Formula: see text] on the height of the potential barrier and the other thermodynamical quantities like temperature and heat capacity. Then, we study the quasinormal modes (QNMs) of 3D black holes in the [Formula: see text] context. For this purpose, we use the WKB approximation method upto third-order corrections. We have shown the perturbation’s decay in corresponding diagrams when the string parameter b changes.

Spectral Geometry of Black Holes in 4D Gauged Supergravity

In this work we show that the area of the event horizon of the Chong–Cvetic–Lu–Pope black hole can be reconstructed in terms of the spectra of the Laplacian on the event horizon. This result, which extends previous works regarding the de Sitter–Kerr–Newman case, points towards a possible description of the black hole degrees of freedom in terms of the spectra of canonical operators defined on the event horizon.

New class of solutions in f(R)-gravity's rainbow and f(R)-gravity: Exact solutions+thermodynamics+quasinormal modes

This paper is devoted to the obtaining of the exact solutions in the framework of modified f(R)-gravity's rainbow(UV completion of General Relativity)/f(R)-gravity and the study of their thermodynamic behavior. In the f(R)-gravity's rainbow, we have analyzed the concept of effective potential barrier by transforming the radial equation of motion into standard Schrodinger form (we should note that scalar field Ψ(x) couples to gravity minimally or non-minimally with coupling constant λ and the gravity representation which is coupled with the scalar field is f(R) not just R). The most important result derived from this study is that gravity's rainbow increases the height of this potential in the exterior region of the event horizon. We also figure out the effect of the coupling constant λ and the f(R) parameter η on the height of the potential barrier and the other thermodynamical quantities like temperature and heat capacity. We have shown that the effect of f(R)-gravity on the temperature adds a coefficient of 1/2 to the cosmological constant.1 We study the quasinormal modes (QNMs) of 3D black holes in the f(R)-gravity's rainbow. For this purpose, we use the WKB approximation method upto third order corrections. We have shown the perturbations decay in corresponding diagrams when the coupling constant λ and rainbow function g(ε) change. We also obtain two different solutions when Ricci scalar is constant. The first one is for a charged slowly rotating toroidal black holes and the second one is for a higher dimensional toroidal black holes inspired by non-commutative geometry. The source for the second one is given by a fluid-type matter with the Gaussian-distribution smeared mass density. In Starobinsky model we show that the charged slowly rotating solution is ill-defined for s2=1 value.

Phase transition and quasinormal modes for charged black holes in 4D Einstein-Gauss-Bonnet gravity * *Supported by the National Natural Science Foundation of China (11605152, 11675139, 51802247) and Outstanding youth teacher programme from Yangzhou University

In four-dimensional Einstein-Gauss-Bonnet (EGB) gravity, we consider the thermodynamic and phase transitions of (charged) AdS black holes. For the negative GB coefficient , the system allows two physical critical points, corresponding to the reentrant phase transition, when the charge . For arbitrary , the system always leads to a van der Waals phase transition. We then study the quasinormal modes (QNMs) of massless scalar perturbations to probe the van der Waals-like phase transition between small and large black holes (SBH/LBH) for (charged) AdS black holes. We find that the signature of this SBH/LBH phase transition in the isobaric process can be detected since the slopes of the QNM frequencies change dramatically in small and large black holes near the critical point. The obtained results further support that QNMs can be a dynamic probe of thermodynamic properties in black holes.

Equilibrium density matrices for the 2D black hole sigma models from an integrable spin chain

This work concerns the quantum Lorentzian and Euclidean black hole non-linear sigma models. For the Euclidean black hole sigma model an equilibrium density matrix is proposed, which reproduces the modular invariant partition function from the 2001 paper of Maldacena, Ooguri and Son. For the Lorentzian black hole sigma model, using its formulation as a gauged SL(2, ℝ) WZW model, we describe the linear and Hermitian structure of its space of states and also propose an expression for the equilibrium density matrix. Our analysis is guided by the results of the study of a certain critical, integrable spin chain. In the scaling limit, the latter exhibits the key features of the Lorentzian black hole sigma model including the same global symmetries, the same algebra of extended conformal symmetry and a continuous spectrum of conformal dimensions.