Black Holes In Arbitrary Dimensions Research Articles

Thermodynamic schemes of charged BTZ-like black holes in arbitrary dimensions

We investigate thermodynamic schemes of charged BTZ-like black holes in arbitrary dimensions, namely higher-dimensional charged black holes in which the electromagnetic sector exhibits the same properties with that of the usual three-dimensional BTZ solution. We first present the Euclidean on-shell action in arbitrary dimensions, inserting a radial cutoff. We then extract the corresponding thermodynamic quantities from the semi-classical partition function in different ensembles and find that there exist two possible thermodynamic schemes, with different outcomes. Regarding the traditional scheme (scheme I), where the length cutoff is identified with the AdS radius, we show that charged BTZ-like black holes are super-entropic, namely they violate the reverse isoperimetric inequality conjecture, and their super-entropicity is strongly connected to a fundamental thermodynamic instability. This class of solutions is the first demonstration of super-entropic black holes which possess second-order critical points and, since thermodynamic instabilities always arise, it is not possible to physically interpret the corresponding van der Waals critical phenomenon in this scheme. In the second scheme (II) where the length cutoff is considered as an independent variable, namely the system respects the conjectured reverse isoperimetric inequality, we show that the solutions are thermodynamically stable in an ensemble where the length cutoff is kept fixed, and hence one can provide an explanation for the van der Waals critical phenomenon. Furthermore, in order to verify the consistency of the second scheme, we study the Joule–Thomson expansion and we extract the Joule–Thomson coefficient, the inversion temperature, the inversion curves, and the isenthalpic curves. The results indicate that this class of AdS black holes can be considered as interacting statistical systems. Additionally, in the D→3 limit we recover the conventional charge BTZ black holes, as well as their thermodynamic properties. Finally, we report a new thermodynamic instability for charged BTZ black holes, as well as their generalization to higher dimensions, which implies that working in an ensemble with fixed length cutoff is mandatory to consistently examine the thermodynamic processes.

Spinorial Wheeler–DeWitt wave functions inside black hole horizons

We revisit the solutions of the Wheeler–DeWitt (WDW) equation inside the horizons of spherical black holes and planar topological black holes in arbitrary dimensions. For these systems, the solutions of the equations are found to have the same form. Therefore, Yeom’s Annihilation-to-nothing interpretation can be applied to each case. We have introduced the Dirac-type WDW equations into quantum cosmology in a recent paper, so we also apply our formulation to the quantum theory of the interior of the black hole in order to obtain the solution of the spinorial wave function. The shape of the wave packet of the spinorial WDW wave function indicates that the variation of Yeom’s interpretation holds in this scheme.

Topology of black hole thermodynamics in Lovelock gravity

In this work, we present a convenient method to perform the topological analysis of black hole thermodynamics. Utilizing the spinodal curve, thermodynamic critical points of a black hole are endowed with a topological quantity, Brouwer degree, which reflects intrinsic properties of the system under smooth deformations. Specially, in our setup, it can be easily calculated without exact solution of critical points. This enables us to conveniently investigate the topological transition between different thermodynamic systems, and give a topological classification for them. In this framework, topology of Lovelock AdS black holes with spherical horizon geometry is explored. Results show that charged black holes in arbitrary dimensions can be classified into the same topology class, whereas the $d=7$ and $d \geq 8$ uncharged black holes are in different topology classes. Moreover, we revisit the relation between different phase structures of these black holes from the viewpoint of topology. Some general topological properties of critical points are also discussed.

Superentropic black hole shadows in arbitrary dimensions

We investigate the shadow behaviors of the superentropic black holes in arbitrary dimensions. Using the Hamilton–Jacobi mechanism, we first obtain the associated null geodesic equations of motion. By help of a spheric stereographic projection, we discuss the shadows in terms of one-dimensional real curves. Fixing the mass parameter m, we obtain certain shapes being remarkably different than four dimensional geometric configurations. We then study theirs behaviors by varying the black hole mass parameter. We show that the shadows undergo certain geometric transitions depending on the spacetime dimension. In terms of a critical value m_c, we find that the four dimensional shadows exhibit three configurations being the D-shape, the cardioid and the naked singularity associated with m>m_c, m=m_c and m<m_c, respectively. We reveal that the D-shape passes to the naked singularity via a critical curve called cardioid. In higher dimensions, however, we show that such transitional behaviors are removed.

Hidden conformal symmetries from Killing towers with an application to large-D/CFT

We generalize the notion of hidden conformal symmetry in Kerr/CFT to Kerr-(A)dS black holes in arbitrary dimensions. We build the SL(2, R) generators directly from the Killing tower, whose Killing tensors and Killing vectors enforce the separability of the equations of motion. Our construction amounts to an explicit relationship between hidden conformal symmetries and Killing tensors: we use the Killing tower to build a novel tensor equation connecting the SL(2,R) Casimir with the radial Klein-Gordon operator. For asymptotically flat black holes in four and five dimensions we recover previously known results that were obtained using the ``near-region'' limit and the monodromy method. We then perform a monodromy evaluation of the Klein-Gordon scalar wave equation for all Kerr-(A)dS black holes, finding explicit forms for the zero mode symmetry generators. We also extend this analysis to the large-dimensional Schwarzschild black hole as a step towards buliding a Large-D/CFT correspondence.

A Komar-like integral for mass and angular momentum of asymptotically AdS black holes in Einstein gravity

The purpose of this paper is to enhance the conventional Komar integral to asymptotically anti-de Sitter (AdS) black holes. In order to do so, we first obtain a potential that is the linear combination of the usual Komar potential with two third-order derivative terms generated by the action of the d’Alembertian operator and the exterior derivative upon a Killing vector. Then this higher-order corrected potential is extended to the Einstein gravity with a negative cosmological constant, yielding the potential that is the linear combination of the usual Komar one with it acted on by the d’Alembertian. It is demonstrated that the surface integral of the improved Komar potential can serve as a formula for conserved charges of asymptotically AdS spacetimes. Finally, to illustrate such a formula, we make use of it to compute the mass and the angular momentum of Schwarzschild-AdS black holes, regular AdS black holes, asymptotically AdS Kerr-Sen black holes, Kerr-NUT-AdS black holes, and Kerr-AdS black holes in arbitrary dimensions. The results are in agreement with the ones in the literature.

Null hypersurface caustics for high-dimensional superentropic black holes

A black hole is superentropic if it violates the reverse isoperimetric inequality. Recently, some studies have indicated that some four dimensional superentropic black holes have the null hypersurface caustics (NHC) outside their event horizons. In this paper, we extend to explore whether or not the NHC exists in the cases of high dimensional superentropic black holes. We consider the singly rotating Kerr-AdS superentropic black holes in arbitrary dimensions and the singly rotating charged superentropic black hole in five-dimensional minimal gauged supergravity, and find that the NHC exists outside the event horizons for these superentropic black holes. Furthermore, the spacetime dimensions and other parameters of black hole, such as the electric charge, have important impact on the NHC inside the horizon. Our results indicate that when the superentropic black hole has the Cauchy horizon, the NHC will also exist inside the Cauchy horizon.

Deflection angle and shadow behaviors of quintessential black holes in arbitrary dimensions

Motivated by M-theory/superstring inspired models, we investigate certain behaviors of the deflection angle and the shadow geometrical shapes of higher dimensional quintessential black holes associated with two values of the dark energy (DE) state parameter, being and . Concretely, we derive the geodesic equation of photons on such backgrounds. Thanks to the Gauss–Bonnet theorem corresponding to the optical metric, we compute the leading terms of the deflection angle in the so-called weak-limit approximation. After that, we inspect the effect of DE and the space–time dimension d on the calculated optical quantities. Introducing DE via the field intensity c and the state parameter ω, we find that the shadow size and the deflection angle increase by increasing values of the field intensity c. However, we observe that the high dimensions decrease such quantities for ω-models exhibiting similar behaviors. Then, we consider the effect of the black hole charge, on these optical quantities, by discussing the associated behaviors. The present investigation recovers certain known results appearing in ordinary four dimensional models.

Notes on the thermodynamics of superentropic AdS black holes

The super-entropic black hole, which possesses a noncompact horizon topology and violates the reverse isoperimetric inequality, has been found to satisfy both the thermodynamic first law and the Bekenstein-Smarr mass formula. In this paper, we first derive a new Christodoulou-Ruffini-like squared-mass formula for the four-dimensional Kerr-Newman-AdS super-entropic black hole, and then establish a set of very simple relations between thermodynamic quantities of the super-entropic Kerr-Newman-AdS$_4$ black hole and its usual counterparts. Using these relations, the thermodynamic quantities of the Kerr-Newman-AdS$_4$ super-entropic black hole can be obtained from those of the usual pro-type by taking the ultra-spinning limit properly. Then these relations are extended to the singly-rotating Kerr-AdS black holes in arbitrary dimensions and the double-rotating charged black hole in the five-dimensional minimal gauged supergravity. It can be inferred that the thermodynamic quantities of all super-entropic black holes obey similar limiting relations to those of their corresponding conventional rotating AdS black holes, and thus can be obtained by taking the ultra-spinning limit appropriately.

Detector response along null geodesics in black hole spacetimes and in a Friedmann-Lemaitre-Robertson-Walker universe

We study the detector's response when moving along an ingoing null geodesic. The backgrounds are chosen to be black hole spacetimes [($1+1$)-dimensional Schwarzschild metric and near-horizon effective metric for any stationary black hole in arbitrary dimensions] as well as a Friedmann-Lemaitre-Robertson-Walker (FLRW) universe. For black holes, the trajectories are defined in Schwarzschild coordinates, and the field modes correspond to a Boulware vacuum, whereas for the FLRW case, the detector is moving along the path defined in original cosmic time and the field modes are related to a conformal vacuum. The analysis is done for three stages (de Sitter, radiation dominated, and matter dominated) of the universe. We find that, although the detector is freely falling, it registered particles in the above-mentioned respective vacuums. We confirm this by different approaches. The detection probability distributions, in all situations, are thermal in nature.

Constraints from accretion onto a Tangherlini\u2013Reissner\u2013Nordstrom black hole

We investigate spherically symmetric, steady state, adiabatic accretion onto a Tangherlini–Reissner–Nordstrom black hole in arbitrary dimensions by using D-dimensional general relativity. We obtain basic equations for accretion and determine analytically the critical points, the critical fluid velocity, and the critical sound speed. We lay emphasis on the condition under which the accretion is possible. This condition constrains the ratio of mass to charge in a narrow limit, which is independent of dimension for large dimension. This condition may challenge the validity of the cosmic censorship conjecture since a naked singularity is eventually produced as the magnitude of charge increases compared to the mass of black hole.

New restrictions on the topology of extreme black holes

We provide bounds on the first Betti number and structure results for the fundamental group of horizon cross-sections for extreme stationary vacuum black holes in arbitrary dimension, without additional symmetry hypotheses. This is achieved by exploiting a correspondence between the associated near-horizon geometries and the mathematical notion of $m$-quasi Einstein metrics, in addition to generalizations of the classical splitting theorem from Riemannian geometry. Consequences are analyzed and refined classifications are given for the possible topologies of these black holes.

Integrability of geodesics in near-horizon extremal geometries: Case of Myers-Perry black holes in arbitrary dimensions

We investigate dynamics of probe particles moving in the near-horizon limit of extremal Myers-Perry black holes in arbitrary dimensions. Employing ellipsoidal coordinates we show that this problem is integrable and separable, extending the results of the odd dimensional case discussed by Hakobyan et al. [Phys. Lett. B 772, 586 (2017).]. We find the general solution of the Hamilton-Jacobi equations for these systems and present explicit expressions for the Liouville integrals and discuss Killing tensors and the associated constants of motion. We analyze special cases of the background near-horizon geometry were the system possesses more constants of motion and is hence superintegrable. Finally, we consider a near-horizon extremal vanishing horizon case which happens for Myers-Perry black holes in odd dimensions and show that geodesic equations on this geometry are also separable and work out its integrals of motion.

Generalized wave operators, weighted Killing fields, and perturbations of higher dimensional spacetimes

We present weighted covariant derivatives and wave operators for perturbations of certain algebraically special Einstein spacetimes in arbitrary dimensions, under which the Teukolsky and related equations become weighted wave equations. We show that the higher dimensional generalization of the principal null directions are weighted conformal Killing vectors with respect to the modified covariant derivative. We also introduce a modified Laplace–de Rham-like operator acting on tensor-valued differential forms, and show that the wave-like equations are, at the linear level, appropriate projections off shell of this operator acting on the curvature tensor; the projection tensors being made out of weighted conformal Killing–Yano tensors. We give off shell operator identities that map the Einstein and Maxwell equations into weighted scalar equations, and using adjoint operators we construct solutions of the original field equations in a compact form from solutions of the wave-like equations. We study the extreme and zero boost weight cases; extreme boost corresponding to perturbations of Kundt spacetimes (which includes near horizon geometries of extreme black holes), and zero boost to static black holes in arbitrary dimensions. In 4D our results apply to Einstein spacetimes of Petrov type D and make use of weighted Killing spinors.

Rotating hairy black holes in arbitrary dimensions

A class of exact rotating black hole solutions of gravity nonminimally coupled to a self-interacting scalar field in arbitrary dimensions is presented. These spacetimes are asymptotically locally anti-de Sitter manifolds and have a Ricci-flat event horizon hiding a curvature singularity at the origin. The scalar field is real and regular everywhere and its effective mass, coming from the nonminimal coupling with the scalar curvature, saturates the Breitenlohner-Freedman bound for the corresponding spacetime dimension. The rotating black hole is obtained by applying an improper coordinate transformation to the static one. Although both spacetimes are locally equivalent, they are globally different, as it is confirmed by the nonvanishing angular momentum of the rotating black hole. It is found that the mass is bounded from below by the angular momentum in agreement with the existence of an event horizon. The thermodynamical analysis is carried out in the grand canonical ensemble. The first law is satisfied and a Smarr formula is exhibited. The thermodynamical local stability of the rotating hairy black holes is established from their Gibbs free energy. However, the global stability analysis establishes that the vacuum spacetime is always preferred over the hairy black hole. Thus, the hairy black hole is likely to decay into the vacuum one for any temperature.

Throat quantization of the Schwarzschild-Tangherlini(-AdS) black hole

By the throat quantization pioneered by Louko and Mäkelä, we derive the mass and area/entropy spectra for the Schwarzschild-Tangherlini-type asymptotically flat or AdS vacuum black hole in arbitrary dimensions. Using the WKB approximation for black holes with large mass, we show that area/entropy is equally spaced for asymptotically flat black holes, while mass is equally spaced for asymptotically AdS black holes. Exact spectra can be obtained for toroidal AdS black holes in arbitrary dimensions including the three-dimensional BTZ black hole.

Soft black hole absorption rates as conservation laws

The absorption rate of low-energy, or soft, electromagnetic radiation by spherically symmetric black holes in arbitrary dimensions is shown to be fixed by conservation of energy and large gauge transformations. We interpret this result as the explicit realization of the Hawking-Perry-Strominger Ward identity for large gauge transformations in the background of a non-evaporating black hole. Along the way we rederive and extend previous analytic results regarding the absorption rate for the minimal scalar and the photon.

Superradiance instability of small rotating AdS black holes in arbitrary dimensions

We investigate the stability of $D$ dimensional singly rotating Myers-Perry-AdS black holes under superradiance against scalar field perturbations. It is well known that small four dimensional rotating or charged Anti-de Sitter (AdS) black holes are unstable against superradiance instability of a scalar field. Recent works extended the existence of this instability to five dimensional rotating charged AdS black holes or static charged AdS black holes in arbitrary dimensions. In this work we analytically prove that, rotating small AdS black holes in arbitrary dimensions also show superradiance instability irrespective of the value of the (positive) angular momentum quantum number. To do this we solve the Klein-Gordon equation in the slow rotation, low frequency limit. By using the asymptotic matching technique, we are able to calculate the real and imaginary parts of the correction terms to the frequency of the scalar field due to the presence of the black hole, confirming the presence of superradiance instability. We see that, unlike in the case of static AdS black holes, the analytical method is valid for rotating AdS black holes for any value of angular momentum number and space-time dimensions. For comparison we derive the corresponding correction terms for Myers-Perry black holes in the black hole bomb formalism in Appendix and see that the results are in agreement.

The universal property of the entropy sum of black holes in all dimensions

It is proposed by Cvetic et al. [1] that the product of all horizon areas for general rotating multi-change black holes has universal expressions independent of the mass. When we consider the product of all horizon entropies, however, the mass will be present in some cases, while another new universal property [2] is preserved, which is more general and says that the sum of all horizon entropies depends only on the coupling constants of the theory and the topology of the black hole. The property has been studied in limited dimensions and the generalization in arbitrary dimensions is not straight-forward. In this Letter, we prove a useful formula, which makes it possible to investigate this conjectured universality in arbitrary dimensions for the maximally symmetric black holes in general Lovelock gravity and f(R) gravity. We also propose an approach to compute the entropy sum of general Kerr–(anti-)de-Sitter black holes in arbitrary dimensions. In all these cases, we prove that the entropy sum depends only on the coupling constants and the topology of the black hole.

On the thermodynamic stability of rotating black holes in higher dimensions—a comparision of thermodynamic ensembles

Thermodynamic potentials relevant to the microcanonical, the canonical and the grand canonical ensembles, associated with rotating black holes in D-dimensions, are analysed and compared. Such black holes are known to be thermodynamically unstable, but the instability is a consequence of a subtle interplay between specific heats and the moments of inertia and it manifests itself differently in the different ensembles. A simple relation between the product of the specific heat and the determinant of the moment of inertia in both the canonical and the grand canonical ensembles is derived. Myers–Perry black holes in arbitrary dimension are studied in detail. All temperature extrema in the microcanonical ensemble are determined and classified. The specific heat and the moment of inertia tensor are evaluated in both the canonical and the grand canonical ensembles in any dimension. All zeros and poles of the specific heats, as a function of the angular momenta, are determined and the eigenvalues of the isentropic moment of inertia tensor are studied and classified. It is further shown that many of the thermodynamic properties of a Myers–Perry black hole in dimensions can be obtained from those of a black hole in D dimensions by sending one of the angular momenta to infinity.