As a charged spinning fermion drops into a charged rotating BTZ black hole, we investigate the laws of thermodynamics and weak cosmic censorship conjecture with and without pressure respectively. For the case without pressure, the first law, second law, as well as the weak cosmic censorship are found to be valid. While for the case with pressure, though the first law is still valid, the second law and the weak cosmic censorship conjecture are found to be violable, depending on the charge, angular momentum, AdS radius, and their variations. In addition, in both cases, the configurations of the extremal black holes are found to be stable since the final states of the extremal black holes are still extremal black holes. While for the near-extremal black holes, their configurations are not stable.
Recently it has been shown that quantum fields can be regular on the inner, Cauchy horizon of a rotating BTZ black hole, which appears to indicate a failure of strong cosmic censorship. We argue that, instead, what these results imply is that the inner horizon remains non-singular when leading-order backreaction of the quantum fields is computed, but, after next-order backreaction is accounted for, it will become singular. Then, strong cosmic censorship will be enforced in the BTZ black hole. We support our claims using a four-dimensional holographic dual of the system, which connects the inst…
We study the phenomena of mass inflation using the Ori model for a rotating BTZ black hole that is sufficiently far from extremality, and show that the right Cauchy horizon ($\mathcal{CH}^+_R$) of the BTZ black hole becomes singular. Motivated by the recent analysis of Dias, Reall, Santos [J. High Energy Phys. 12 (2019) 097], we choose the retrograde quasinormal modes to govern the decay of perturbations exterior to the black hole. The resulting model captures the violation of the strong cosmic censorship conjecture near extremality. On the other hand, far from extremality, the $\mathcal{CH}^+…
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…
We investigate the stability of the inner horizon of a rotating BTZ black hole. We show that linear perturbations arising from smooth initial data are arbitrarily differentiable at the inner horizon if the black hole is sufficiently close to extremality. This is demonstrated for scalar fields, for massive Chern-Simons fields, for Proca fields, and for massive spin-2 fields. Thus the strong cosmic censorship conjecture is violated by a near-extremal BTZ black hole in a large class of theories. However, we show that a weaker "rough" version of the conjecture is respected. We calculate the renorm…
As charged fermions drop into the BTZ black holes, we check the laws of thermodynamics and weak cosmic censorship conjecture in the normal phase space and extended phase space, where the cosmological parameter and renormalization length are regarded as extensive quantities. In the normal phase space, the first and second law of thermodynamics as well as the weak cosmic censorship are valid. While in the extended phase space, though the first law and weakcosmic censorship conjecture are still valid, the second law is dependent on the variation of the renormalization energy $dK$. In addition, in…
We analyze the gravitational perturbations induced by particles falling into a three dimensional, asymptotically AdS black hole geometry. More specifically, we solve the linearized perturbation equations obtained from the geodesic motion of a ring-like distribution of test particles in the BTZ background. This setup ensures that the U(1) symmetry of the background is preserved. The non-asymptotic flatness of the background raises difficulties in attributing the significance of energy and angular momentum to the conserved quantities of the test particles. This issue is well known but, to the be…
The weak cosmic censorship conjecture in the near-extremal BTZ black hole has been tested by the test particles and fields. It was claimed that this black hole could be overspun. In this paper, we review the thermodynamics and weak cosmic censorship conjecture in BTZ black holes by the scattering of the 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 the entropy, we test the weak cosmic censorship conjecture by evaluating the minimum values of the function $f…
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…
Investigating the quasinormal modes of a massive scalar field on the 3-dimensional black string (3dBS), we study the strong cosmic censorship (SCC) conjecture for the 3dBS in the T-dual relationship with the 3-dimensional rotating anti-de-Sitter (BTZ) black hole. It is shown that even though geometries of the two spacetimes are quite different, such as asymptotically AdS for the BTZ black hole and asymptotically flat for the 3dBS, the BTZ black hole and the 3dBS share similar properties for the SCC. Concretely speaking, the SCC conjecture can be violated even for asymptotically flat spacetime,…
An exotic Banados-Teitelboim-Zanelli (BTZ) black hole has an angular momentum larger than its mass in three dimension (3D), which suggests the possibility that cosmic censorship could be violated if angular momentum is extracted by the Penrose process. In this paper, we propose a mass formula for the exotic BTZ black hole and show no violation of weak cosmic censorship in the gedanken process above by understanding properly its mass formula. Unlike the other black holes, the total energy of the exotic BTZ black hole is represented by the angular momentum instead of the mass, which supports a b…
Recent work has shown that the entropy of the non-rotating BTZ black hole can be derived from a dual conformal description at any spatial location. In this followup it is shown that a dual conformal description exists at any spatial location for the rotating BTZ black hole as well. As in the non-rotating case, two copies of the central charge $c^{\pm} = 3\ell/2G$ are recovered and the microcanonical Cardy formula yields the correct Bekenstein-Hawking entropy.
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.
We obtain rotating black hole solutions to the novel 3D Gauss-Bonnet theory of gravity recently proposed. These solutions generalize the BTZ metric and are not of constant curvature. They possess an ergoregion and outer horizon, but do not have an inner horizon. We present their basic properties and show that they break the universality of thermodynamics present for their static charged counterparts, whose properties we also discuss. Extending our considerations to higher dimensions, we also obtain novel 4D Gauss-Bonnet rotating black strings.
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 discuss the effect of small statistical thermal fluctuations around the equilibrium on the thermodynamics of small non-rotating BTZ black hole. This is done by evaluating the leading-order corrections to the thermodynamical equation of states, namely, entropy, free energy, internal energy, pressure, enthalpy, Gibbs free energy and specific heat quantitatively. In order to analyze the effect of perturbations on the thermodynamics, we plot various graphs and compare corrected and non-corrected thermodynamic quantities with respect to event horizon radius of non-rotating BTZ bla…
We test the validity of cosmic censorship in the rotating anti-de Sitter black hole. For this purpose, we investigate whether the extremal black hole can be overspun by the particle absorption. The particle absorption will change the mass and angular momentum of the black hole, which is analyzed using the Hamilton-Jacobi equations consistent with the laws of thermodynamics. We have found that the mass of the extremal black hole increases more than the angular momentum. Therefore, the outer horizon of the black hole still exists, and cosmic censorship is valid.
Rotating and/or charged black hole spacetimes possess a Cauchy horizon, beyond which Einstein's equations of General Relativity cease to be deterministic. This led to the formulation of the Strong Cosmic Censorship conjecture that such horizons become irregular under field perturbations. We consider linear field perturbations of rotating and electrically-charged (Kerr-Newman-de Sitter) black holes in a universe with a positive cosmological constant. By calculating the quasinormal modes for scalar and fermion fields, we provide evidence for the existence of weak solutions to Einstein's equation…
For the BTZ black hole in the Einstein gravity, a statistical entropy has been calculated to be equal to the Bekenstein-Hawking entropy. In this paper, the statistical entropy of the BTZ black hole in the higher curvature gravity is calculated and shown to be equal to the one derived by using the Noether charge method. This suggests that the equivalence of the geometrical and statistical entropies of the black hole is retained in the general diffeomorphism invariant theories of gravity. A relation between the cosmic censorship conjecture and the unitarity of the conformal field theory on the b…
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.
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.
We show that a noncommutative massless scalar probe can dress a naked singularity in $AdS_3$ spacetime, consistent with the weak cosmic censorship. The dressing occurs at high energies, which is typical at the Planck scale. Using a noncommutative duality, we show that the dressed singularity has the geometry of a rotating BTZ black hole which satisfies all the laws of black hole thermodynamics. We calculate the entropy and the quasi-normal modes of the dressed singularity and show that the corresponding spacetime can be quantum mechanically complete. The noncommutative duality also gives rise …
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 this paper, we investigate the validity of the weak cosmic censorship conjecture(WCCC) for a rotating linear dilaton black hole from two different methods. By using the classsical ingoing test particle method, we obtain the same results as given in the new version of gedanken experiment recently proposed by Wald. We find that even for this rotating linear dilaton black hole the Iyer-Wald formalism is still functioning. By comparing these two methods, we find that the same result will be obtained in both cases up to first order. The nearly extremal black hole can be overspun, while the extre…
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…
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…
We analyse vacuum decay in rotating BTZ black hole spacetimes with the thin wall approximation. Possible parameter regions for the vacuum decay are clarified. We find that the nucleation rate is dominated by the bounce solution with the static shell configuration. The nucleation rate of the static shell decreases with the mass of the initial black hole. For a larger/smaller value of the initial black hole, the nucleation rate can be smaller/larger than that of the Coleman De Luccia vacuum decay in the pure AdS spacetime. Through the vacuum decay, the black hole gains its mass and loses the hor…
Slowly rotating charged BTZ black hole solutions in Palatini Chern-Simons gravity
Instituto de Física Corpuscular (IFIC), CSIC‐Universitat de València（粒子物理研究所 (IFIC)，西班牙瓦伦西亚大学）；Universidade Federal do Ceará (UFC)（塞阿拉联邦大学）；Federal University of Rio Grande do Norte（北里奥格兰德联邦大学）；International Institute of Physics, Federal University of Rio Grande do Norte（北里奥格兰德联邦大学国际物理研究所）；Universidade Federal da Paraíba（帕拉伊巴联邦大学）
Following Bekenstein's suggestion that the horizon area of a black hole should be quantized, the discrete spectrum of the horizon area has been investigated in various ways. By considering the quasinormal mode of a black hole, we obtain the transition frequency of the black hole, analogous to the case of a hydrogen atom, in the semiclassical limit. According to Bohr's correspondence principle, this transition frequency at large quantum number is equal to classical oscillation frequency. For the corresponding classical system of periodic motion with this oscillation frequency, an action variabl…
During the last few years, exact solutions that describe black holes that are bound to a two-brane in a four dimensional anti-de Sitter bulk have been constructed. In situations wherein there is a negative cosmological constant on the brane, for large masses, these solutions are exactly the rotating BTZ black holes on the brane and, in fact, describe rotating BTZ black strings in the bulk. We evaluate the canonical entropy of a free and massless scalar field (at the Hawking temperature) around the rotating BTZ black string using the brick wall model. We explicitly show that the Bekenstein-Hawk…
By applying Newman's algorithm, the AdS_3 rotating black hole solution is ``derived'' from the nonrotating black hole solution of Banados, Teitelboim, and Zanelli (BTZ). The rotating BTZ solution derived in this fashion is given in ``Boyer-Lindquist-type'' coordinates whereas the form of the solution originally given by BTZ is given in a kind of an ``unfamiliar'' coordinates which are related to each other by a transformation of time coordinate alone. The relative physical meaning between these two time coordinates is carefully studied. Since the Kerr-type and Boyer-Lindquist-type coordinates …
We revisit the non-rotating massive BTZ black hole within a pseudo-Riemannian symmetric space context. Using classical symmetric space techniques we find that every such space intrinsically carries a regular Poisson structure whose symplectic leaves are para-hermitian symmetric surfaces. We also obtain a global expression of the metric yielding a dynamical description of the black hole from its initial to its final singularity.
In this work, we consider rotating BTZ black hole in three dimensions which is dual of one dimensional holographic superconductors. We applied higher order corrections of the entropy, which interpreted as quantum corrections, to the thermodynamics quantities and study modified thermodynamics. We investigate stability of rotating BTZ black hole under effects of higher order quantum corrections, and find that they affect stability of black hole. So, the small black hole has some instabilities and critical points due to the quantum effects. We also study effect of correction terms on the dual pic…
We have considered the divergence structure in the brick-wall model for the statistical mechanical entropy of a quantum field in thermal equilibrium with a black hole which {\it rotates}. Especially, the contribution to entropy from superradiant modes is carefully incorporated, leading to a result for this contribution which corrects some previous errors in the literature. It turns out that the previous errors were due to an incorrect quantization of the superradiant modes. Some of main results for the case of rotating BTZ black holes are that the entropy contribution from superradiant modes i…
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, $dE=TdS+ΩdJ+Φdq+P_{r}dA$.
The recent proposal of Maggiore that the periodicity of a black hole may be the origin of area quantization law is analyzed in the context of three dimensional black holes. We use the period of motion of an outgoing wave which is shown to be related to the vibrational frequency of the perturbed black hole, to quantize the horizon area of rotating and non-rotating BTZ black holes. It is shown that the equally spaced area spectrum takes the same form as the obtained in the literature using the quasinormal mode analysis for both metrics. Using this method, we do not need to use the small angular …
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…
In this paper, we study the effect of ultra-high energy collisions of two particles with different energies near the horizon of a 2+1 dimensional BTZ black hole (BSW effect). We find that the particle with the critical angular momentum could exist inside the outer horizon of BTZ black hole regardless of the particle energy. Therefore, for the non-extremal BTZ black hole, the BSW process is possible on the inner horizon with the fine tuning of parameters which are characterized by the motion of particle. While for the extremal BTZ black hole, the particle with the critical angular momentum coul…
We present exact solutions describing rotating, inhomogeneous dust with generic initial data in 2+1 dimensional AdS spacetime and show how they are smoothly matched to the Banados-Teitelboim-Zanelli (BTZ) solution in the exterior. The metrics, which are the rotational analogues of the 2+1 dimensional LeMaitre-Tolman-Bondi (LTB) family, are described by their angular momentum and one additional constant which, together with the angular momentum, determines the energy density of the dust cloud. The weak energy condition gives a constraint on the angular momentum profile inside the cloud. Solutio…
We investigate the thermodynamic equilibrium states of a rotating thin shell, i.e., a ring, in a (2+1)-dimensional spacetime with a negative cosmological constant. The inner and outer regions with respect to the shell are given by the vacuum anti-de Sitter and the rotating Bañados-Teitelbom-Zanelli spacetimes, respectively. The first law of thermodynamics on the thin shell, together with three equations of state for the pressure, the local inverse temperature and the thermodynamic angular velocity of the shell, yields the entropy of the shell, which is shown to depend only on its gravitational…
We consider gedanken experiments to destroy an extremal or near-extremal BTZ black hole by throwing matter into the horizon. These black holes are vacuum solutions to (2+1)-dimensional gravity theories, and are asymptotically $\mathrm{AdS}_3$. Provided the null energy condition for the falling matter, we prove the following---(i) in a Mielke-Baekler model without ghost fields, when torsion is present, an extremal BTZ black hole can be overspun and becomes a naked conical singularity; (ii) in 3-dimensional Einstein gravity and chiral gravity, which both live in torsionless limits of Mielke-Baek…
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.
According to Bohr-Sommerfeld quantization rule, an equally spaced horizon area spectrum of a static, spherically symmetric black hole was obtained under an adiabatic invariant action. This method can be extended to the rotating black holes. As an example, we apply this method to the rotating BTZ black hole and obtain the quantized spectrum of the horizon area. It is shown that the area spectrum of the rotating BTZ black hole is equally spaced and irrelevant to the rotating parameter, which is consistent with the Bekenstein conjecture. Specifically, the derivation do not need the quasinormal fr…
We demonstrate an optical realization for the rotating BTZ black hole using the recent popular photon fluid model in an optical vortex but with a new proposed expression for the optical phase. We also give the numerical realization for the optical vortex to ensure that it can be generated experimentally. Different from the earlier suggestions for the analogue rotating black holes, our proposal includes an inner horizon in the analogue black hole structure. Such structure can keep for a long distance for the convenience of observing analogue Hawking or Penrose radiations.
In a (2+1)-dimensional spacetime with a negative cosmological constant, the thermodynamics and the entropy of an extremal rotating thin shell, i.e., an extremal rotating ring, are investigated. The outer and inner regions are taken to be the Bañados-Teitelbom-Zanelli (BTZ) spacetime and the vacuum ground state anti-de Sitter (AdS) spacetime, respectively. By applying the first law of thermodynamics to the extremal shell one shows that its entropy is an arbitrary function of the gravitational area $A_+$ alone, $S=S(A_+)$. When the shell approaches its own gravitational radius $r_+$ and turns in…
We consider the behaviour of a quantum scalar field on three-dimensional Euclidean backgrounds: Anti-de Sitter space, the regular BTZ black hole instanton and the BTZ instanton with a conical singularity at the horizon. The corresponding heat kernel and effective action are calculated explicitly for both rotating and non-rotating holes. The quantum entropy of the BTZ black hole is calculated by differentiating the effective action with respect to the angular deficit at the conical singularity. The renormalization of the UV-divergent terms in the action and entropy is considered. The structure …
In this paper we investigate the Sagnac effect by calculating the difference in travel time and phase shift observed for photon beams counter--propagating in a rotating interferometer on a BTZ black hole solution in the context of scale-dependent gravity, which describes the field around a massive static and rotating object in $2+1$ gravity.
