Narrow Results

We study the wave equation for a massive scalar in three-dimensional AdS-black hole spacetimes to understand the unitarity issues in a semiclassical way. Here we introduce four interesting spacetimes: the non-rotating BTZ black hole (NBTZ), pure AdS spacetime (PADS), massless BTZ black hole (MBTZ), and extremal BTZ black hole (EBTZ). Our method is based on the potential analysis and solving the wave equation to find the condition for the frequency ω exactly. In the NBTZ case, one finds the quasinormal (complex and discrete) modes which signals for a non-unitary evolution. Real and discrete modes are found for the PADS case, which means that it is unitary obviously. On the other hand, we find real and continuous modes for the two extremal black holes of MBTZ and EBTZ. It suggests that these could be candidates for the unitary system.

There has been some recent controversy regarding the Ruppeiner metrics that are induced by Reissner–Nordström (and Reissner–Nordström-like) black holes. Most infamously, why does this family of metrics turn out to be flat, how is this outcome to be physically understood, and can/should the formalism be suitably modified to induce curvature? In this paper, we provide a novel interpretation of this debate. For the sake of maximal analytic clarity and tractability, some supporting calculations are carried out for the relatively simple model of a rotating BTZ black hole.

Motivated by the possibility of formulating a strings/black hole correspondence in AdS space, we extract the Hagedorn behavior of thermal AdS₃ bosonic string from 1-loop partition function of SL(2,R) WZW model. We find that the Hagedorn temperature is monotonically increasing as the AdS radius shrinks, reaches a maximum of order of string scale set by the unitarity bound of the CFT for internal space. The resulting density of states near the Hagedorn temperature resembles the form as for strings in flat space and is dominated by the space-like long string configurations. We also examine strings on BTZ background obtained through SL(2, Z) transformation. We find a tachyonic divergence for a BTZ black hole of string scale size.

A Sagnac type experiment is analyzed in the most well-known (2+1)-dimensional Bañados, Teitelboim and Zanelli (BTZ) spacetime and discussed vis-a-vis corresponding results in (3+1)-dimensional spacetime. The angular velocity of locally non-rotating observer has formally been predicted using Sagnac effect. Occurrence of arbitrarily large Sagnac delay (SD) for geodesic motion is observed for extreme BTZ black hole universally as its remarkable feature.

We show that there is no superradiance for the Dirac field in the rotating BTZ black hole if the field vanishes at infinity. Then we outline the calculation of the expression for the renormalized energy–momentum tensor, the effective action as well as the heat kernel for the Dirac field for the BTZ black hole. Finally, we point out how to construct the Hartle–Hawking–Israel state for the real scalar field in the non-rotating BTZ black hole in two and three dimensions.

We investigate the existence and stability of both the timelike and null circular orbits for a (2 + 1)-dimensional charged BTZ black hole in Einstein-nonlinear Maxwell gravity with a negative cosmological constant. The stability analysis of orbits is performed to study the possibility of chaos in geodesic motion for a special case of black hole so-called conformally invariant Maxwell spacetime. The computations of both proper time Lyapunov exponent $({\lambda }_p)$ and coordinate time Lyapunov exponent $({\lambda }_c)$ are useful to determine the stability of these circular orbits. We observe the behavior of the ratio $({\lambda }_p/{\lambda }_c)$ as a function of radius of circular orbits for the timelike case in view of different values of charge parameter. However, for the null case, we calculate only the coordinate time Lyapunov exponent $({\lambda }_c)$ as there is no proper time for massless test particles. More specifically, we further analyze the behavior of the ratio of ${\lambda }_{\mathrm{\text{Null}}}$ to angular frequency $({\mathrm{\Omega }}_c)$, so-called instability exponent as a function of charge $(q)$ and parameter related to cosmological constant $(l)$ for the particular values of other parameters.

Various observations from cosmic microwave background radiation (CMBR), type Ia supernova and baryon acoustic oscillations (BAO) are strongly suggestive of an accelerated expansion of the universe which can be explained by the presence of mysterious energy known as dark energy. The quintessential matter coupled with gravity minimally is considered one of the possible candidates to represent the presence of such dark energy in our universe. In view of this scenario, we study the geodesic of massless particles as well as massive particles around a (2 + 1)-dimensional BTZ black hole (BH) spacetime surrounded by the quintessence. The effect of parameters involved in the deflection of light by such a BH spacetime is investigated in detail. The results obtained are then compared with a usual non-rotating BTZ BH spacetime.

In this paper we consider a BTZ black hole with minimum length which has been introduced through the probability density of the ground state of the hydrogen atom. We analyzed the effect of the minimum length by calculating the thermodynamic quantities such as temperature and entropy and verified the stability of the black hole by computing the specific heat capacity.

For the three-dimensional BTZ black hole we consider a Selberg type zeta function. We indicate how special values of its logarithm correspond to certain thermodynamic quantities associated with the black hole.

We study a finite temperature string in curved space, especially in AdS₃ and BTZ black hole background. We extract Hagedorn behavior of strings and argue thermodynamic properties in thermal AdS₃ as well as in BTZ black hole background. In particular, we find the Hagedorn temperature of string on AdS₃, which depends on the AdS₃ curvature scale. We also find a tachyonic divergence for a BTZ black hole of string scale.

Tunneling of scalar particles across the event horizon of rotating BTZ black hole is investigated using the Generalized Uncertainty Principle to study the corrected Hawking temperature and entropy in the presence of quantum gravity effects. We have determined explicitly the various correction terms in the entropy of rotating BTZ black hole including the logarithmic term of the Bekenstein–Hawking entropy $(S_{\mathrm{\text{BH}}})$, the inverse term of $S_{\mathrm{\text{BH}}}$ and terms with inverse powers of $S_{\mathrm{\text{BH}}}$, in terms of properties of the black hole and the emitted particles — mass, energy and angular momentum. In the presence of quantum gravity effects, for the emission of scalar particles, the Hawking radiation and thermodynamics of rotating BTZ black hole are observed to be related to the metric element, hence to the curvature of space–time.

The motivation behind this study is to enumerate the leading order corrections to the thermodynamics of BTZ black hole (named after three scientists; Banados, Teitelboim, and Zanelli). We first analyze the effect of quantum corrections (motivated from string theory and loop quantum gravity) on various thermodynamic variables for uncharged and stationary BTZ black hole. We, later on, endow charges and rotations to the same black hole and rederive all the expressions once again. The comparative analysis is done between the corrected and uncorrected thermodynamics via plots.

The Hawking radiation of BTZ black hole is investigated based on generalized uncertainty principle effect by using Hamilton–Jacobi method and Dirac equation. The tunneling probability and the Hawking temperature of the spin-1/2 particles of the BTZ black hole are investigated using the modified Dirac equation based on the GUP. The modified Hawking temperature for fermion crossing the black hole horizon includes the mass parameter of the black hole, angular momentum, energy and also outgoing mass of the emitted particle. Besides, considering the effect of GUP into account, the modified Hawking radiation of massless particle from a BTZ black hole is investigated using Damour and Ruffini method, tortoise coordinate transformation and modified Klein–Gordon equation. The relation between the modified Hawking temperature obtained by using Damour–Ruffini method and the energy of the emitted particle is derived. The original Hawking temperature is also recovered in the absence of quantum gravity effect. There is a possibility of negative Hawking temperature for emission of Dirac particles under quantum gravity effects.

We investigate the space–time of a spinning cosmic string in conformal invariant gravity, where the interior consists of a gauged scalar field. We find exact solutions of the exterior of a stationary spinning cosmic string, where we write the metric as $g_{\mu \nu }={\omega }^2{\tilde{g}}_{\mu \nu }$, with $\omega$ a dilaton field which contains all the scale dependences. The “unphysical” metric ${\tilde{g}}_{\mu \nu }$ is related to the $(2+1)$-dimensional Kerr space–time. The equation for the angular momentum $J$ decouples, for the vacuum situation as well as for global strings, from the other field equations and delivers a kind of spin-mass relation. For the most realistic solution, $J$ falls off as $\sim \frac{1}{r}$ and ${\partial }_{r}J\to 0$ close to the core. The space–time is Ricci flat. The formation of closed timelike curves can be pushed to space infinity for suitable values of the parameters and the violation of the weak energy condition can be avoided. For the interior, a numerical solution is found. This solution can easily be matched at the boundary on the exterior exact solution by special choice of the parameters of the string. This example shows the power of conformal invariance to bridge the gap between general relativity and quantum field theory.

We re-examine Hawking radiation for a nonrotating $(2+1)$-dimensional Bañados–Teitelboim–Zanelli (BTZ) black hole and evaluate the transmission probability of tunneling through the barrier of the event horizon employing the standard method of WKB approximation. Our results are presented for both uncharged and charged cases. We also explore the associated thermodynamics in terms of Hawking temperature and provide estimates of black hole parameters like the surface gravity and entropy.

We evaluate the energy distribution associated with the (2+1)-dimensional rotating BTZ black hole. The energy–momentum complexes of Landau–Lifshitz and Weinberg are employed for this computation. Both prescriptions give exactly the same form of energy distribution. Therefore, these results provide evidence in support of the claim that, for a given gravitational background, different energy–momentum complexes can give identical results in three dimensions, as is the case in four dimensions.

Recently Hod proposed a lower bound on the relaxation time of a perturbed thermodynamic system. For gravitational systems this bound transforms into a condition on the fundamental quasinormal frequency. We test the bound in some space–times whose quasinormal frequencies are calculated exactly, as the three-dimensional BTZ black hole, the D-dimensional de Sitter space–time, and the D-dimensional Nariai space–time. We find that for some of these space–times their fundamental quasinormal frequencies do not satisfy the bound proposed by Hod.

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 conjecture. The structure and locations of the apparent horizons of the black holes are also determined. It is interesting to see that, in the static limit and when N = 2, one can retrieve 2+1 BTZ black hole solutions.

In this paper we investigate vector particles' Hawking radiation from a Banados–Teitelboim–Zanelli (BTZ) black hole. By applying the Wentzel–Kramers–Brillouin (WKB) approximation and the Hamilton–Jacobi ansatz to the Proca equation, we obtain the tunneling spectrum of vector particles. The expected Hawking temperature is recovered.

In this paper, we construct thin-shell wormholes in (2 + 1)-dimensions from noncommutative BTZ black hole by applying the cut-and-paste procedure implemented by Visser. We calculate the surface stresses localized at the wormhole throat by using the Darmois–Israel formalism and we find that the wormholes are supported by matter violating the energy conditions. In order to explore the dynamical analysis of the wormhole throat, we consider that the matter at the shell is supported by dark energy equation of state (EoS) p = ωρ with ω < 0. The stability analysis is carried out of these wormholes to linearized spherically symmetric perturbations around static solutions. Preserving the symmetry we also consider the linearized radial perturbation around static solution to investigate the stability of wormholes which was explored by the parameter β (speed of sound).