Motivated by many worthwhile paper about (2 + 1)-dimensional BTZ black holes, we generalize them to to (n + 1)-dimensional solutions, so called BTZ-like solutions. We show that the electric field of BTZ-like solutions is the same as (2 + 1)-dimensional BTZ black holes, and also their lapse functions are approximately the same, too. By these similarities, it is also interesting to investigate the geometric and thermodynamics properties of the BTZ-like solutions. We find that, depending on the metric parameters, the BTZ-like solutions may be interpreted as black hole solutions with inner (Cauchy) and outer (event) horizons, an extreme black hole or naked singularity. Then, we calculate thermodynamics quantities and conserved quantities, and show that they satisfy the first law of thermodynamics. Finally, we perform a stability analysis in the canonical ensemble and show that the BTZ-like solutions are stable in the whole phase space.
We find solution to the metric function f(r)=0 of charged BTZ black hole making use of the Lambert function. The condition of extremal charged BTZ black hole is determined by a non-linear relation of M_e(Q)=Q^2(1-\ln Q^2). Then, we study the entropy of extremal charged BTZ black hole using the entropy function approach. It is shown that this formalism works with a proper normalization of charge Q for charged BTZ black hole because AdS_2 x S^1 represents near-horizon geometry of the extremal charged BTZ black hole. Finally, we introduce the Wald's Noether formalism to reproduce the entropy of t…
We study the thermodynamics and the thermodynamic geometries of charged rotating BTZ (CR-BTZ) black holes in (2+1)-gravity. We investigate the thermodynamics of these systems within the context of the Weinhold and Ruppeiner thermodynamic geometries and the recently developed formalism of geometrothermodynamics (GTD). Considering the behavior of the heat capacity and the Hawking temperature, we show that Weinhold and Ruppeiner geometries cannot describe completely the thermodynamics of these black holes and of their limiting case of vanishing electric charge. In contrast, the Legendre invarianc…
We generate from the static charged BTZ black hole a family of spinning charged solutions to the Einstein-Maxwell equations in 2+1 dimensions. These solutions go over, in a suitable limit, to self-dual spinning charged solutions, which are horizonless and regular, with logarithmically divergent mass and spin. To cure this divergence, we add a topological Chern-Simons term to the gauge field action. The resulting self-dual solution is horizonless, regular, and asymptotic to the extreme BTZ black hole.
Thermodynamics of the BTZ black hole in noncommutative geometry is studied. We work out the Hawking temperature and entropy which reduce to their commutative limits when the noncommutativity parameter tends to zero. We also discuss the range of validity of the Hawking area law in the noncommutative case and provide graphical analysis. We see that the law is not valid unless the outer horizon is very large.
We present the thermodynamics of a charged and rotating BTZ black holes here. In particular, we derive expressions for various macroscopic thermal quantities such as entropy, Hawking temperature, Helmholtz free energy, internal energy, enthalpy, Gibbs free energy, and specific heat. To study the effects of small statistical thermal fluctuations around the equilibrium on thermodynamics, we calculated the leading-order corrections to the various thermodynamical potentials of charged and rotating BTZ black hole and do comparative analysis for the fixed values of charge and angular momentum.
In this paper we study the first law of thermodynamics for the (2+1) dimensional charged BTZ black hole considering a pair of thermodinamical systems constructed with the two horizons of this solution. We show that these two systems are similar to the right and left movers of string theory and that the temperature associated with the black hole is the harmonic mean of the temperatures associated with these two systems.
In the present paper, the quantum corrections to the temperature, entropy and specific heat capacity of the charged non-rotating BTZ black hole are studied by generalized uncertainty principle in tunneling formalism. It is shown that quantum corrected entropy would be of the form of predicted entropy in quantum gravity theories like string theory and loop quantum gravity.
In this paper we will show that using the cosmological constant as a new thermodynamical state variable, the differential and integral mass formulas of the first law of thermodynamics for asymptotic flat spacetimes can be extended to (2+1) dimensional charged BTZ black holes and charged de Sitter space.
Due to the asymptotic structure of the black hole solution, there are two different thermodynamic schemes for the charged Banados-Teitelboim-Zanelli (BTZ) black hole. In one scheme, the charged BTZ black hole is super-entropic, while in the other, it is not (the reverse isoperimetric inequality is saturated). In this paper, we investigate the thermodynamic curvature of the charged BTZ black hole in different coordinate spaces. We find that in both schemes, the thermodynamic curvature is always positive, which may be related to the information of repulsive interaction between black hole molecul…
We find an exact nonstatic charged BTZ-like solutions, in ($N$+1)-dimensional Einstein gravity in the presence of negative cosmological constant and a nonlinear Maxwell field defined by a power $s$ of the Maxwell invariant, which describes the gravitational collapse of charged null fluid in an anti-de Sitter background. Considering the situation that a charged null fluid injects into the initially an anti-de Sitter spacetime, we show that a black hole form rather than a naked singularity, irrespective of spacetime dimensions, from gravitational collapse in accordance with cosmic censorship con…
The well-known $(2+1)$-dimensional Reissner-Nordstrom (BTZ) black hole can be generalized to three dimensional Einstein-nonlinear electromagnetic field, motivated from obtaining a finite value for the self-energy of a pointlike charge. Considering three types of nonlinear electromagnetic fields coupled with Einstein gravity, we derive three kinds of black hole solutions which their asymptotic properties are the same as charged BTZ solution. In addition, we calculate conserved and thermodynamic quantities of the solutions and show that they satisfy the first law of thermodynamics. Finally, we p…
In this manuscript, we investigate the thermal properties of the rotating charged BTZ black hole under the gravity's rainbow (GR) and generalized uncertainty principle (GUP) formalism. At first, we study the GR-corrected thermal quantities according to the usual Heisenberg algebra. Then, we consider a deformed algebra that leads to a change in the Heisenberg uncertainty principle and compare the Hawking temperature, entropy, thermodynamical volume, pressure, and heat capacity functions with the previous results. Thus, we understand and interpret the quantum effects on the BTZ black hole.
We obtain a (3+3)-dimensional global flat embedding of the generalized (2+1) charged Bañados-Teitelboim-Zanelli black holes in massive gravity. We also study the local free-fall temperatures for freely falling observers starting from rest and investigate the effect of the charge and graviton mass in free-fall temperatures.
The charged BTZ black hole is characterized by a power-law curvature singularity generated by the electric charge of the hole. The curvature singularity produces ln r terms in the asymptotic expansion of the gravitational field and divergent contributions to the boundary terms. We show that these boundary deformations can be generated by the action of the conformal group in two dimensions and that an appropriate renormalization procedure allows for the definition of finite boundary charges. In the semiclassical regime the central charge of the dual CFT turns out to be that calculated by Brown …
In this paper, we study different cases of the charged rotating BTZ black hole with reference to their horizons. For the existence of these cases conditions on mass, charge and angular momentum of the black hole are obtained. It is also shown that the Einstein field equations for the charged rotating BTZ black hole at the horizon can be expressed as first law of thermodynamics, $dE=TdS+ΩdJ+Φdq+P_{r}dA$.
As is already known, a spacetime horizon acts like a boundary of a thermal system an we can associate with it notions as temperature and entropy. Following the work of M. Akbar, in this paper we will show how it is possible to interpret the field equation of a charged BTZ black hole near horizon as a thermodynamic identity dE=TdS+PdA+PhidQ, where Phi is the electric potential and Q is the electric charge of BTZ black hole. These results indicate that the field equations for the charged BTZ black hole possess intrinsic thermodynamic properties near horizon.
We study the Klein-Gordon equation of a scalar field conformally coupled to a charged BTZ black hole. The background metric is obtained by coupling a non-linear and conformal invariant Maxwell field to (2+1) gravity. We show that the radial part is generally solved by a Heun function and, in the pure gravity limit, by a hypergeometric function.
It is known that traversable wormhole can exist in General Relativity only if its throat contains some exotic matter. In this paper, we obtain $(2+1)$-dimensional (horizonless) charged magnetic brane without (curvature) singularity. Then, we consider a nontrivial local transformation to grant a global rotation to spacetime. After that, we generalize magnetic brane to higher dimensional solutions and use the cut-and-paste method to construct higher dimensional charged BTZ-like rotating wormholes such a way that they reduce to charged magnetic BTZ solution in three dimensions, exactly. We also s…
We provide a discussion on a light ray in a charged black hole solution in massive gravity. To serve the purpose, we exploit the optical geometry of the black hole solution and find the Gaussian curvature in weak gravitational lensing. Furthermore, we discuss the deflection angle of the light ray in both plasma and non-plasma mediums using the Gauss-Bonnet theorem on the black hole. We also analyze the Regge--Wheeler equation and derive rigorous bounds on the greybody factors of linearly charged massive BTZ black hole. We also study the shadow or silhouette generated by charged massive BTZ bla…
In this paper, we calculate the topological entanglement entropy of the BTZ black hole and find that it coincides with that for fractional quantum Hall state. So the BTZ black holes have the same topological order with the fractional quantum Hall state. This fact indicate that the BTZ black holes have long-range entanglement.
Using the AdS/CFT correspondence we calculate the explicit form of the entanglement entropy for the charged BTZ black hole. The leading term in the large temperature expansion of the entropy function for this black hole reproduces its Bekenstein-Hawking entropy and the subleading term, representing the first corrections due to quantum entanglement, behaves as a logarithm of the BH entropy.
We find the Gregory-Laflamme $s$-mode instability of the non-rotating BTZ black hole in new massive gravity. This instability shows that the BTZ black hole could not exist as a stable static solution to the new massive gravity. For non-rotating BTZ black string in four dimensions, however, it is demonstrated that the BTZ black string can be stable against the metric perturbation.
In three dimensions, a phase transition occurs between the non-rotating BTZ black hole and the massless BTZ black hole. Further, introducing the mass of a conical singularity, we show that a transition between the non-rotating BTZ black hole and thermal AdS space is also possible.
BTZ black holes are excellent laboratories for studying black hole thermodynamics which is a bridge between classical general relativity and quantum nature of gravitation. In addition, three-dimensional gravity could have equipped us for exploring some of the ideas behind the two dimensional conformal field theory based on the $AdS_{3}/CFT_{2}$. Considering the significant interests in these regards, we examine charged BTZ black holes. We consider the system contains massive gravity with energy dependent spacetime to enrich the results. In order to make high curvature (energy) BTZ black holes …
Noncommutative geometry is an established potential candidate for including quantum phenomena in gravitation. We outline the formalism of Hopf algebras and its connection to the algebra of infinitesimal diffeomorphisms. Using a Drinfeld twist we deform spacetime symmetries, algebra of vector fields and differential forms leading to a formulation of noncommutative Einstein equations. We study a concrete example of charged BTZ spacetime and deformations steaming from the so called angular twist. The entropy of the noncommutative charged BTZ black hole is obtained using the brick-wall method. We …
Motivated by the wide applications of BTZ black holes and interesting results of gravity's rainbow, we consider three dimensional rainbow solutions and investigate their thermodynamic properties. In addition to investigate black holes thermodynamics related to AdS/CFT correspondence, one may regard gravity's rainbow to to encode quantum gravity effects into the black hole solutions. We take into account the various models of linear and nonlinear electrodynamics and study their effects on the gravity's rainbow spacetime. We also examine thermal stability and find that obtained three dimensional…
We construct an axially symmetric solution of Eddington-inspired Born-Infeld gravity coupled to an electromagnetic field in 2+1 dimensions including a (negative) cosmological constant term. This is achieved by using a recently developed mapping procedure that allows to generate solutions in certain families of metric-affine gravity theories starting from a known seed solution of General Relativity, which in the present case corresponds to the electrically charged Banados-Teitelboim-Zanelli (BTZ) solution. We discuss the main features of the new configurations, including the modifications to th…
We consider charged rotating BTZ black holes in noncommutative space by use of Chern-Simons theory formulation of $2+1$ dimensional gravity. The noncommutativity between the radial and the angular variables is introduced through the Seiberg-Witten map for gauge fields, and the deformed geometry to the first order in the noncommutative parameter is derived. It is found that the deformation also induces nontrivial torsion, and the Einstein-Cartan theory appears to be a suitable framework to investigate the equations of motion. Though the deformation is indeed nontrivial, the deformed and the ori…
Physical Features of Geometrically Deformed Anisotropic Charged Three-dimensional BTZ Black Holes
Institute of Mathematics, University of the Punjab（旁遮普大学数学研究所）；Faculty of Symbiotic Systems Science, Fukushima University（福岛大学共生系统科学学院）；Department of Mathematics, College of Science, King Saud University（国王沙特大学理学院数学系）；Department of Mathematics, Quaid-i-Azam University（真纳大学数学系）；Research Center of Astrophysics and Cosmology, Khazar University（哈扎尔大学天体物理学与宇宙学研究中心）
Motivated by the wide applications of thermal stability and phase transition, we investigate thermodynamic properties of charged BTZ black holes. We apply the standard method to calculate the heat capacity and the Hessian matrix and find that thermal stability of charged BTZ solutions depends on the choice of ensemble. To overcome this problem, we take into account cosmological constant as a thermodynamical variable. By this modification, we show that the ensemble dependency is eliminated and thermal stability conditions are the same in both ensembles. Then, we generalize our solutions to the …
In this paper we study the first law of thermodynamics for the (2+1) dimensional rotating charged BTZ black hole considering a pair of thermodinamical systems constructed with the two horizons of this solution. We show that these two systems are similar to the right and left movers of string theory and that the temperature associated with the black hole is the harmonic mean of the temperatures associated with these two systems.
We study the dynamical behavior of the BTZ (Banados-Teitelboim-Zanelli) black hole with the low-energy string effective action. The perturbation analysis around the BTZ black hole reveals a mixing between the dilaton and other fields. Introducing the new gauge (dilaton gauge), we disentangle this mixing completely and obtain one decoupled dilaton equation. We obtain the decay rate $Γ$ of BTZ black hole.
We show that the 3D charged Banados-Teitelboim-Zanelli (BTZ) black hole solution interpolates between two different 2D AdS spacetimes: a near-extremal, near-horizon AdS_2 geometry with constant dilaton and U(1) field and an asymptotic AdS_2 geometry with a linear dilaton. Thus, the charged BTZ black hole can be considered as interpolating between the two different formulations proposed until now for AdS_2 quantum gravity. In both cases the theory is the chiral half of a 2D CFT and describes, respectively, Brown-Hennaux-like boundary deformations and near-horizon excitations. The central charge…
In order to classify and understand the spacetime structure, investigation of the geodesic motion of massive and massless particles is a key tool. So the geodesic equation is a central equation of gravitating systems and the subject of geodesics in the black hole dictionary attracted much attention. In this paper, we give a full description of geodesic motions in three-dimensional spacetime. We investigate the geodesics near charged BTZ black holes and then generalize our prescriptions to the case of massive gravity. We show that electric charge is a critical parameter for categorizing the geo…
The strong cosmic censorship conjecture, whose validation asserts the deterministic nature of general relativity, has been studied for charged BTZ black holes in three dimensional general relativity, as well as for Nth order pure Lovelock gravity in d=2N+1 spacetime dimensions. Through both analytical and numerical routes, we have computed the ratio of the imaginary part of the quasi-normal mode frequencies with the surface gravity at the Cauchy horizon. The lowest of which corresponds to the key parameter associated with violation of strong cosmic censorship conjecture. Our results demonstrat…
It is well known that ($2+1$) dimensional charged BTZ (Banados, Teitelboim, Zanelli) black hole can be overcharged by a charged scalar field and a charged particle in contrast to their analogues in ($3+1$) and higher dimensions. In this regard, it may play an important role to understand more deeply the properties of the ($2+1$)-dimensional charged black hole in the Einstein-Gauss-Bonnet (EGB) gravity. In this paper, we test the validity of the weak cosmic censorship conjecture for the ($2+1$)-dimensional charged black hole in novel EGB theory derived recently by Henniger et. al (2021). We sho…
The entropy of the charged BTZ black hole horizon is described by the Cardy-Verlinde formula. We then compute the self-gravitational corrections to the Cardy-Verlinde formula of the charged BTZ black hole in the context of Keski-Vakkuri, Kraus and Wilczek (KKW) analysis. The self-gravitational corrections to the entropy as given by the Cardy-Verlinde formula are found to be positive. This result provides evidence in support of the claim that the holographic bound is not universal in the framework of two-dimensional gravity models.
We extend our recent discussion of four-dimensional black holes bound to a two-brane to include a negative cosmological constant on the brane. We find that for large masses, the solutions are precisely BTZ black holes on the brane, and BTZ `black strings' in the bulk. For smaller masses, there are localized black holes which look like BTZ with corrections that fall off exponentially. We compute when the maximum entropy configuration changes from the black string to the black hole. We also present exact solutions describing rotating black holes on two-branes which are either asymptotically flat…
In this paper, we study the Hawking temperature of the BTZ black hole based on the purely topological method proposed by Robson, Villari, and Biancalana (RVB) [Phys. Rev. D 99, 044042 (2019)]. The Hawking temperature of the charged rotating BTZ black hole can be accurately derived by this topological method. We also calculate the Hawking temperature of the BTZ black hole in massive gravity. Because the metric function of the BTZ black hole in massive gravity has a mass term, the corresponding Hawking temperature cannot be derived unless an integral constant is added.
This study is purposed to derive the equation of motion for geodesics in vicinity of spacetime of a (2 + 1)-dimensional charged BTZ black hole. In this paper, we solve geodesics for both massive and massless particles in terms of Weierstrass elliptic and Kleinian sigma hyper-elliptic functions. Then we determine different trajectories of motion for particles in terms of conserved energy and angular momentum and also using effective potential.
BTZ black holes provide excellent frameworks for studying theories that are at the interface of classical and quantum gravity. In this paper we couple the Riemannian spacetime with the bumblebee field, in the background of massive gravity, which produces the violation of spontaneous Lorentz symmetry. In this setup we construct a large family of static vacuum BTZ black hole solutions. We study the asymptotic behaviour of curvature invariants and show that our resulting solutions describe asymptotically AdS (2+1)-dimensional BTZ black holes with negative cosmological constant. For positive cosmo…
We introduce an analog model for the conformally coupled scalar field on the BTZ black hole. The model is based on the propagation of acoustic waves in a Laval nozzle. Since the BTZ black hole is not a globally hyperbolic spacetime, the dynamics of the scalar field is not well defined until extra boundary conditions are prescribed at its spatial infinity. We show that quasinormal modes (QNMs) satisfying Dirichlet, Neumann, and Robin boundary conditions in the BTZ black hole can be interpreted in terms of ordinary QNMs defined with respect to an appropriately extended nozzle. We also discuss th…
A recent paper [M. Kamata and T. Koikawa, Phys. Lett. {\bf B353} (1995) 196.] claimed to obtain the charged version of the $(2+1)$-dimensional spinning $BTZ$ black hole solution by assuming a (anti-) self dual condition imposed on the electric and magnetic fields. We point out that the angular momentum and mass diverge at spatial infinity and as a consequence the solution is unphysical
BTZ black hole is interpreted as exact solution of 3d higher spin gauge theory. Solutions for free massless fields in BTZ black hole background are constructed with the help of the star-product algebra formalism underlying the formulation of 3d higher spin theory. It is shown that a part of higher spin symmetries remains unbroken for special values of the BTZ parameters.
We derive an exact expression for the partition function of the Euclidean BTZ black hole. Using this, we show that for a black hole with large horizon area, the correction to the Bekenstein-Hawking entropy is $-3/2 log(Area)$, in agreement with that for the Schwarzschild black hole obtained in the canonical gravity formalism and also in a Lorentzian computation of BTZ black hole entropy. We find that the right expression for the logarithmic correction in the context of the BTZ black hole comes from the modular invariance associated with the toral boundary of the black hole.
In this work, we present a study to probe the nature of interactions between black hole microstructures for the case of the BTZ black holes. Even though BTZ black holes without any angular momentum or electric charge thermodynamically behave as an ideal gas, i.e. with non-interacting microstructures; in the presence of electric charge or angular momentum, BTZ black holes are associated with repulsive interactions among the microstructures. We extend the study to the case of exotic BTZ black holes with mass $M = αm + γ\frac{j}{l}$ and angular momentum $J=αj + γl m$, for arbitrary values of $ (α…
We investigate thermodynamics of the BTZ black hole in new massive gravity explicitly. For $m^2\ell^2>1/2$ with $m^2$ the mass parameter of fourth-order terms and $\ell^2$ AdS$_3$ curvature radius, the Hawking-Page phase transition occurs between the BTZ black hole and AdS (thermal) soliton. For $m^2\ell^2<1/2$, however, this transition unlikely occurs but a phase transition between the BTZ black hole and the massless BTZ black hole is possible to occur. We may call the latter as the inverse Hawking-Page phase transition and this transition is favored in the new massive gravity.
It is shown how to transform the three dimensional BTZ black hole into a four dimensional cylindrical black hole (i.e., black string) in general relativity. This process is identical to the transformation of a point particle in three dimensions into a straight cosmic string in four dimensions.
In this paper we consider the generalized uncertainty principle (GUP) in the tunneling formalism via Hamilton-Jacobi method to determine the quantum-corrected Hawking temperature and entropy for noncommutative BTZ black hole. In our results we obtain several types of corrections including the expected logarithmic correction to the area entropy associated with the noncommutative BTZ black holes. We also show that the area entropy product of the noncommutative BTZ black holes is dependent on mass and by analyzing the nature of the specific heat capacity we have observed that the noncommutative B…
The emission rate of fermions from 2+1 dimensional BTZ black holes is shown to have a form which can be reproduced from a conformal field theory at finite temperature. The rate obtained for fermions is identical to the rate of non-minimally coupled fermions emitted from a five dimensional black hole, whose near horizon geometry is BTZ X M, where M is a compact manifold.
In this paper, we study the thermodynamics and phase transition of a BTZ black hole in a finite space region, namely a cavity. By imposing a temperature-fixed boundary condition on the wall of the cavity and evaluating the Euclidean action, we derive the thermodynamic quantities and then construct the first law of thermodynamics for a static and neutral BTZ black hole, a rotating BTZ black hole and a charged BTZ black hole, respectively. We prove that heat capacities of these three types of black holes are always non-negative. Considering a grand canonical ensemble, we find that the non-extrem…
