In this paper, the curvature structure of a (2+1)-dimensional black hole in the massive-charged-Born-Infeld gravity is investigated. The metric that we consider is characterized by four degrees of freedom which are the mass and electric charge of the black hole, the mass of the graviton field, and a cosmological constant. For the charged and neutral cases separately, we present various constraints among scalar polynomial curvature invariants which could invariantly characterize our desired spacetimes. Specially, an appropriate scalar polynomial curvature invariant and a Cartan curvature invariant which together could detect the black hole horizon would be explicitly constructed. Using algorithms related to the focusing properties of a bundle of light rays on the horizon which are accounted for by the Raychaudhuri equation, a procedure for isolating the black hole parameters, as the algebraic combinations involving the curvature invariants, would be presented. It will be shown that this technique could specially be applied for black holes with zero electric charge, contrary to the cases of solutions of lower-dimensional non-massive gravity. In addition, for the case of massive (2+1)-dimensional black hole, the irreducible mass, which quantifies the maximum amount of energy which could be extracted from a black hole would be derived. Therefore, we show that the Hawking temperatures of these black holes could be reduced to the pure curvature properties of the spacetimes. Finally, we comment on the relationship between our analysis and the novel roles it could play in numerical quark-gluon plasma simulations and other QCD models and also black hole information paradox where the holographic correspondence could be exploited.
We calculate the interior volume for the three-dimensional Banados-Teitelboim-Zanelli black hole in this paper. To that end, we obtain the volume functional and numerically find a path to extremize it, before choosing a spacelike hypersurface to get an asymptotic analytical expression for the interior volume based on the characteristics of the path.
We study quasinormal modes (QNMs) of massive Klein-Gordon fields in static Bañados-Teitelboim-Zanelli (BTZ) black holes in terms of ladder operators constructed from spacetime conformal symmetries. Because the BTZ spacetime is locally isometric to the three-dimensional anti-de Sitter spacetime, ladder operators, which map a solution of the massive Klein-Gordon equation into that with different mass squared, can be constructed from spacetime conformal symmetries. In this paper, we apply the ladder operators to the QNMs of the Klein-Gordon equations in the BTZ spacetime. We demonstrate that the …
We consider a collision of two dust thin shells with a high center-of-mass (CM) energy including their self-gravity in a Bañados-Teitelboim-Zanelli (BTZ) spacetime. The shells divide the BTZ spacetime into three domains and the domains are matched by the Darmois-Israel junction conditions. We treat only the collision of two shells which corotate with a background BTZ spacetime because of the junction conditions. The counterpart of the corotating shell collision is a collision of two particles with vanishing angular momenta. We compare the dust thin shell collision and the particle collision in…
We examine the Banados-Teitelboim-Zanelli (BTZ) black hole in terms of the information geometry and consider what kind of quantum information produces the black hole metric in close connection with the anti-de Sitter space/conformal field theory (AdS/CFT) correspondence. We find a Hessian potential that exactly produces both the BTZ metric and the entanglement entropy formula for CFT_{1+1} at a finite temperature. Taking a free-falling frame near the event horizon is a key procedure to derive these exact results. We also find an alternative Hessian potential that produces the same BTZ metric, …
In the context of three-dimensional gravity with torsion, the concepts of standard and "exotic" Banados-Teitelboim-Zanelli black holes are generalized by going over to black holes with torsion. This approach provides a unified insight into thermodynamics of black holes, with or without torsion.
We study linear scalar perturbations of black holes in two-dimensional (2D) gravity models with a particular emphasis on Jackiw-Teitelboim (JT) gravity. We obtain an exact expression of the quasinormal mode frequencies for single horizon black holes in JT gravity and then verify it numerically using the Horowitz-Hubeny method. For a 2D Reissner-Nordström like solution, we find that the massless scalar wave equation reduces to the confluent Heun equation using which we calculate the Hawking spectra. Finally, we consider the dimensionally reduced Bañados-Teitelboim-Zanelli (BTZ) black hole and o…
In 2+1 dimensional Chern-Simons gravity, Wilson loops in the three dimensional Anti de Sitter group, $SO(2,2)$, reproduce the spinning black hole of Bañados, Teitelboim and Zanelli (BTZ) by naturally duplicating the necessary identification of points of a four dimensional globally $SO(2,2)$ invariant space in which the hole appears as an embedding.
The electrogravity transformation is applied to the three-dimensional Einstein field equations to obtain new multi-parameter families of black hole solutions. The Bañados-Teitelboim-Zanelli black hole is shown to be a special case of one of these families. The causal structure, associated matter, as well as the mechanical and thermodynamical properties of some of the solutions are discussed.
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.
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.
Quasi-local energies for constantly accelerating observers in Bañados, Teitelboim, and Zanelli (BTZ), Schwarzschild and Schwarzschild-de Sitter spacetimes are derived. The energies are expressed in terms of acceleration, cosmological constant, and area, quantities measurable by the observers. Based on results from quantum fields in curved spacetime for the redshifted Hawking temperature, entropy and thermodynamic-like laws are briefly explored in the three spacetimes.
We examine the connection between three dimensional gravity with negative cosmological constant and two-dimensional CFT via the Chern-Simons formulation. A set of generalized spectral flow transformations are shown to yield new sectors of solutions. One implication is that the microscopic calculation of the entropy of the Banados-Teitelboim-Zanelli (BTZ) black hole is corrected by a multiplicative factor with the result that it saturates the Bekenstein-Hawking expression.
The cosmological constant is treated as a thermodynamical parameter in the framework of two-dimensional dilaton gravity. We find that the cosmological constant behaves as a U(1) charge with a confining potential, and that such potentials require a novel Born-Infeld boundary term in the action. The free energy and other thermodynamical quantities of interest are derived, from first principles, in a way that is essentially model-independent. We discover that there is always a Schottky anomaly in the specific heat and explain its physical origin. Finally, we apply these results to specific exampl…
The three dimensional black hole solutions of Bañados, Teitelboim and Zanelli (BTZ) are dimensionally reduced in various different ways. Solutions are obtained to the Jackiw-Teitelboim theory of two dimensional gravity for spinless BTZ black holes, and to a simple extension with a non-zero dilaton potential for black holes of fixed spin. Similar reductions are given for charged black holes. The resulting two dimensional solutions are themselves black holes, and are appropriate for investigating exact ``S-wave'' scattering in the BTZ metrics. Using a different dimensional reduction to the strin…
We calculate the quasinormal modes and associated frequencies of the Banados, Zanelli and Teitelboim (BTZ) non-rotating black hole. This black hole lives in 2+1-dimensions in an asymptotically anti-de Sitter spacetime. We obtain exact results for the wavefunction and quasi normal frequencies of scalar, electromagnetic and Weyl (neutrino) perturbations.
We compute the group element of SO(2,2) associated with the spinning black hole found by Bañados, Teitelboim and Zanelli in (2+1)-dimensional anti-de Sitter space-time. We show that their metric is built with SO(2,2) gauge invariant quantities and satisfies Einstein's equations with negative cosmological constant everywhere except at $r=0$. Moreover, although the metric is singular on the horizons, the group element is continuous and possesses a kink there.
The Einstein-Maxwell equations with a negative cosmological constant in 2+1 spacetime dimensions discussed by Banados, Teitelboim and Zanelli are solved by assuming a self(anti-self)dual equation. The solution describes an electrically charged extreme black hole with an angular momentum.
We study physical properties of constant curvature black holes (CCBHs) in Einstein anti-de Sitter (AdS) gravity. These objects, which are locally AdS throughout the space, are constructed from identifications of global AdS spacetime, in a similar fashion as Banados-Teitelboim-Zanelli (BTZ) black hole in three dimensions. We find that, in dimensions equal or greater than four, CCBHs have zero mass and angular momentum. Only in odd dimensions we are able to associate a nonvanishing conserved quantity to these solutions, which corresponds to the vacuum (Casimir) energy of the spacetime.
The charged black hole of Banados, Teitelbiom and Zanelli is studied in extended gravitational thermodynamics where there is a dynamical pressure and volume. It is a simple example of a super-entropic black hole, violating the reverse isoperimetric inequality. It is proven that this property implies that its specific heat at constant volume is negative, signalling a new kind of fundamental instability for black holes. It is conjectured that this instability is present for other super-entropic black holes, and this is demonstrated numerically for a large family of known solutions.
Motivated by several pieces of evidence, in order to show that extreme black holes cannot be obtained as limits of non-extremal black holes, in this article we calculate explicitly quasinormal modes for Bañados, Teitelboim and Zanelli (BTZ) extremal black hole and we showed that the imaginary part of the frequency is zero. We obtain exact result for the scalar an fermionic perturbations. We also showed that the frequency is bounded from below for the existence of the normal modes (non-dissipative modes).
The entropy of stationary black holes has recently been calculated by a number of different approaches. Here we compare the Noether charge approach (defined for any diffeomorphism invariant Lagrangian theory) with various Euclidean methods, specifically, (i) the microcanonical ensemble approach of Brown and York, (ii) the closely related approach of Bañados, Teitelboim, and Zanelli which ultimately expresses black hole entropy in terms of the Hilbert action surface term, (iii) another formula of Bañados, Teitelboim and Zanelli (also used by Susskind and Uglum) which views black hole entropy as…
We give circularly symmetric solutions for null fluid collapse in 2+1-dimensional Einstein gravity with a cosmological constant. The fluid pressure $P$ and energy density $ρ$ are related by $P=kρ$ $(k\le 1)$. The long time limit of the solutions are black holes whose horizon structures depend on the value of $k$. The $k=1$ solution is the Banados-Teitelboim-Zanelli black hole metric in the long time static limit, while the $k<1$ solutions give other, `hairy' black hole metrics in this limit.
We derive the Bekenstein-Hawking entropy formula for four and five dimensional non-supersymmetric black holes (which include the Schwarzchild ones) by counting microscopic states. This is achieved by first showing that these black holes are U-dual to the three-dimensional black hole of Banados-Teitelboim-Zanelli and then counting microscopic states of the latter following Carlip's approach. Higher than five dimensional black holes are also considered. We discuss the connection of our approach to the D-brane picture.
The Bañados-Teitelboim-Zanelli (BTZ) black hole metric solves the three-dimensional Einstein's theory with a negative cosmological constant as well as all the generic higher derivative gravity theories based on the metric; as such it is a universal solution. Here, we find, in all generic higher derivative gravity theories, new universal non-Einsteinian solutions obtained as Kerr-Schild type deformations of the BTZ black hole. Among these, the deformed non-extremal BTZ black hole loses its event horizon while the deformed extremal one remains intact as a black hole in any generic gravity theory…
In this paper we investigate an exact spectrum of quasi normal modes (QNMs) for perturbations of a scalar field coupled non-minimally with the Einstein tensor of an uncharged, non-rotating Banados, Teitelboim, and Zanelli (BTZ) black hole in three-dimensional spacetime. Due to the geometry around the black hole, the scalar field encounters an effective potential barrier. We study this potential numerically and derive exact numerical results for the greybody factors (GFs) and discuss their profiles in terms of the coupling constant and black hole parameters. We then proceed to derive the Hawkin…
The thermodynamic properties of the (2+1)-dimensional non-rotating black hole of Bañados, Teitelboim and Zanelli are discussed. The first quantum correction to the Bekenstein-Hawking entropy is evaluated within the on-shell Euclidean formalism, making use of the related Chern-Simons representation of the 3-dimensional gravity. Horizon and ultraviolet divergences in the quantum correction are dealt with a renormalization of the Newton constant. It is argued that the quantum correction due to the gravitational field shrinks the effective radius of a hole and becomes more and more important as so…
With the recent discovery that many aspects of black hole thermodynamics can be effectively reduced to problems in three spacetime dimensions, it has become increasingly important to understand the ``statistical mechanics'' of the (2+1)-dimensional black hole of Banados, Teitelboim, and Zanelli (BTZ). Several conformal field theoretic derivations of the BTZ entropy exist, but none is completely satisfactory, and many questions remain open: there is no consensus as to what fields provide the relevant degrees of freedom or where these excitations live. In this paper, I review some of the unresol…
Conformal field theories corresponding to two-dimensional electrically charged black holes and to two-dimensional anti-de Sitter space with a covariantly constant electric field are simply constructed as $SL(2,R)/Z$ WZW coset models. The two-dimensional electrically charged black holes are related by Kaluza-Klein reduction to the 2+1-dimensional rotating black hole of Banados, Teitelboim and Zanelli, and our construction is correspondingly related to its realization as a WZW model. Four-dimensional spacetime solutions are obtained by tensoring these two-dimensional theories with $SU(2)/Z(m)$ c…
The quantum stress tensor $<T_{μν}>$ is calculated in the 2+1 dimensional black hole found by Banados, Teitelboim, and Zanelli. The Greens function, from which $<T_{μν}> $ is derived, is obtained by the method of images. For the non-rotating black hole, it is shown that $<T_{μν}>$ is finite on the event horizon, but diverges at the singularity. For the rotating solution, the stress tensor is finite at the outer horizon, but diverges near the inner horizon. This suggests that the inner horizon is quantum mechanically unstable against the formation of a singularity.
The entropy of a Bañados, Teitelboim, and Zanelli black hole in topologically massive gravity had been given with the form inconsistent with the Bekenstein-Hawking entropy. In the paper, we provide a consistent statistical interpretation for the entropy, and confirm it to be thermodynamic entropy by preserving the first and second laws. As a novel extension, the logarithmic correction to the black hole entropy is also discussed.
We computed the statistical entropy of nonextremal 4D and extremal 5D Calabi-Yau black holes and found exact agreement with the Bekenstein-Hawking entropy. The computation is based on the fact that the near-horizon geometry of equivalent representations contains as a factor the Bañados-Teitelboim-Zanelli black hole and on subsequent use of Strominger's proposal generalizing the statistical count of microstates of the BTZ black hole due to Carlip.
Some judiciously chosen local curvature scalars can be used to invariantly characterize event horizons of black holes in $D > 3$ dimensions, but they fail for the three dimensional Bañados-Teitelboim-Zanelli (BTZ) black hole since all curvature invariants are constant. Here we provide an invariant characterization of the event horizon of the BTZ black hole using the curvature invariants of codimension one hypersurfaces instead of the full spacetime. Our method is also applicable to black holes in generic dimensions but is most efficient in three, four, and five dimensions. We give four dimensi…
We obtain (3+1) and (3+2) dimensional global flat embeddings of (2+1) uncharged and charged black strings, respectively. In particular, the charged black string, which is the dual solution of the Banados-Teitelboim-Zanelli black holes, is shown to be embedded in the same global embedding Minkowski space structure as that of the (2+1) charged de Sitter black hole solution.
In this paper, by means of regularisation procedure via $r\to \sqrt{r^2+l_0^2}$ (where $l_0$ can play the role of zero point length), we first modify the gravitational and electromagnetic potentials in two dimensions and then we solve the Einstein field equations to end up with an exact and regular black hole solution in three dimensions with a negative cosmological constant. We show that, the black hole solution is asymptotically AdS, non-singular at the origin and, under specific conditions, it has a flat de Sitter core at the origin. As a special case, we obtain the charged Banados-Teitelbo…
I review the classical and quantum properties of the (2+1)-dimensional black hole of Ba{ñ}ados, Teitelboim, and Zanelli. This solution of the Einstein field equations in three spacetime dimensions shares many of the characteristics of the Kerr black hole: it has an event horizon, an inner horizon, and an ergosphere; it occurs as an endpoint of gravitational collapse; it exhibits mass inflation; and it has a nonvanishing Hawking temperature and interesting thermodynamic properties. At the same time, its structure is simple enough to allow a number of exact computations, particularly in the quan…
We discuss quantum properties of the single-exterior, geon-type black (and white) holes that are obtained from the Kruskal spacetime and the spinless Banados-Teitelboim-Zanelli hole via a quotient construction that identifies the two exterior regions. For the four-dimensional geon, the Hartle-Hawking type state of a massless scalar field is thermal in a limited sense, but there is a discrepancy between Lorentzian and Riemannian derivations of the geon entropy. For the three-dimensional geon, the state induced for a free conformal scalar field on the conformal boundary is similarly thermal in a…
Using the fact that theories of gravity with asymptotically three-dimensional anti-de Sitter geometries have dual descriptions as two-dimensional conformal field theories (CFTs), we present the first study in field theory of the thermodynamic volume of various black hole solutions. We explain in general two-dimensional CFT terms why the presence of a thermodynamic volume can render certain black hole solutions "super-entropic". Super-entropicity simply results from the fact that the Cardy formula, which gives the gravitational Bekenstein-Hawking entropy, can over-count the CFT entropy. The exa…
We examine an Unruh-DeWitt particle detector coupled to a scalar field in three-dimensional curved spacetime, within first-order perturbation theory. We first obtain a causal and manifestly regular expression for the instantaneous transition rate in an arbitrary Hadamard state. We then specialise to the Bañados-Teitelboim-Zanelli black hole and to a massless conformally coupled field in the Hartle-Hawking vacuum. A co-rotating detector responds thermally in the expected local Hawking temperature, while a freely-falling detector shows no evidence of thermality in regimes that we are able to pro…
Some thermodynamic properties of the Bañados-Teitelboim-Zanelli (BTZ) black hole are studied to get the effective dimension of its corresponding statistical model. For this purpose, we make use of the geometrical approach to the thermodynamics: Considering the black hole as a thermodynamic system with two thermodynamic variables (the mass $M$ and the angular momemtum $J$), we obtain two-dimensional Riemannian thermodynamic geometry described by positive definite Ruppeiner metric. From the thermodynamic curvature we find that the extremal limit is the critical point. The effective spatial dimen…
We introduce a set of scalar fields as test fields to study the dynamical behaviors of the BTZ (Banados-Teitelboim-Zanelli) black hole. These include minimally coupled scalar, conformally coupled scalar, dilaton, and tachyon. To calculate the decay rate of the BTZ black hole, we consider both the Dirichlet boundary condition at spatial infinity and the stability condition. It turns out that the tachyon may be a relevant field to get information of the BTZ black hole.
In the current study, authors present the comprehensive analysis of the Anti-de Sitter/Boundary Conformal Field Theory (AdS/BCFT) correspondence for Lovelock theory of second order in the presence of canonical (and real) scalar field non-minimally coupled to modified gravitation sector. Authors consider the special case with three dimensional BTZ (Banados-Teitelboim-Zanelli) black hole and dual 2D Conformal Field Theory with the additional boundary for higher dimensional AdS spacetime. Moreover, for the given case additional boundary profile was investigated, as well as the holographic renorma…
Generalizations of the Black Hole geometry of Bañados, Teitelboim and Zanelli (BTZ) are presented. The theory is three-dimensional vacuum Einstein theory with a negative cosmological constant. The $n$-black-hole solution has $n$ asymptotically anti-de Sitter ``exterior" regions that join in one ``interior" region. The geometry of each exterior region is identical to that of a BTZ geometry; in particular, each contains a black hole horizon that surrounds (as judged from that exterior) all the other horizons. The interior region acts as a closed universe containing $n$ black holes. The initial s…
The regularization procedure for getting the four-dimensional nontrivial Einstein-Gauss-Bonnet effective description of gravity and its Lovelock generalization has been recently developed. Here we propose the regularization for the three-dimensional gravity, which is based on the rescaling of the coupling constants and, afterward, taking the limit $D \to 3$. We obtain the generalization of the Bañados-Teitelboim-Zanelli solution in the presence of the higher curvature (Gauss-Bonnet and Lovelock) corrections of any order. The obtained general solution shows a peculiar behavior: The event horizo…
By applying Newman's method, 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 coordinates is carefully studied by evaluating angular momentum per unit mass, angular velocity, surface g…
Exciting peculiarities of Planck-scale physics have immediate effects on the Bekenstein-Hawking radiation emitted from black holes (BHs). In this paper, using the tunneling formalism, we determine the Bekenstein-Hawking temperature for the vector particles from a backreacted black hole (BBH) constructed from a conformal scalar field surrounded by a BTZ (Banados-Teitelboim-Zanelli) BH. Then, under the effect of the generalized uncertainty principle, we extend our calculations for scalar particles to understand the effects of quantum gravity. Then, we calculate an evaporation time for the BBH, t…
We examine whether we can make a black hole in Fisher information spacetime and what kind of quantum states produce the black hole solution in terms of the anti-de Sitter spacetime/conformal field theory correspondence. Here we focus on the Banados-Teitelboim-Zanelli black hole. There exists a mathematical representation of entanglement spectra that define the Fisher geometry as the black hole spacetime. We find that this representation is quite similar to the entanglement spectra in a conformal field theory at finite temperature except for minor corrections, and then the inverse temperature c…
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 …
Some aspects of the rotating three-dimensional Einstein-Anti-de-Sitter black hole solution, constructed recently by Banados, Teitelboim and Zanelli are discussed. It is shown explicitly that this black hole represents the most general black hole type solution of the Einstein-Anti-de-Sitter theory. The interpretation of one of the integrals of motion as the spin is discussed. Its physics relies on the topological structure of the black hole manifold, and the notion of simultaneity of space-like separated intervals. The relationship of the black hole solution to string theory on a $2 + 1$ dimens…
In this paper we calculate leading order correction due to small statistical fluctuations around equilibrium, to the Bekenstein-Hawking entropy formula for the Achucarro-Oritz black hole, which is the most general two-dimensional black hole derived from the three-dimensional rotating Banados-Teitelboim-Zanelli black hole. Then we obtain the same correction to the Cardy-Verlinde entropy formula (which is supposed to be an entropy formula of conformal field theory in any dimension).
We investigate the string theory on three dimensional black holes discovered by Bañados, Teitelboim and Zanelli in the framework of conformal field theory. The model is described by an orbifold of the $\widetilde{SL}(2,R)$ WZW model. The spectrum is analyzed by solving the level matching condition and we obtain winding modes. We then study the ghost problem and show explicit examples of physical states with negative norms. We discuss the tachyon propagation and the target space geometry, which are irrelevant to the details of the spectrum. We find a self-dual T-duality transformation reversing…
We construct a kind of thermal potential and then put the black hole thermodynamic system in it. In this regard, some thermodynamic properties of the black hole are related to the geometric characteristics of the thermal potential. Driven by the intrinsic thermodynamic fluctuations, the behavior of the black hole in the thermal potential is stochastic. With the help of solving the Fokker-Planck equation analytically, we obtain the discrete energy spectrum of Schwarzschild and Banados-Teitelboim-Zanelli (BTZ) black holes in the thermal potential. For Schwarzschild black hole, the energy spectru…
Motivated by extended black hole thermodynamics, we generalize the Rényi entropy of charged holographic conformal field theories (CFTs) in $d$-dimensions. Specifically, following (1807.09215), we extend the quench description of the Rényi entropy of globally charged holographic CFTs by including pressure variations of charged hyperbolically sliced anti de Sitter black holes. We provide an exhaustive analysis of the new type of charged Rényi entropy, where we find an interesting interplay between a parameter controlling the pressure of the black hole and its charge. A field theoretic interpreta…
In this paper we extend the quasitopological electromagnetism, recently introduced by H.-S. Liu et al. [arXiv:1907.10876], to arbitrary dimensions by introducing a fundamental $p$-form field. This allows us to construct new dyonic black hole solutions in odd dimensions, as well as regular $D$-dimensional black holes and solitons. The three-dimensional system consists of a Maxwell field interacting with a scalar field, leading to a deformation of the Bañados-Teitelboim-Zanelli black hole. We present the general formulas defining the black hole solutions in arbitrary dimensions in Lovelock theor…
