Dimensional BTZ Black Hole Research Articles

Quasinormal modes of charged BTZ black holes

We investigate the scalar field equation in a (2+1) -dimensional charged BTZ black hole. The quasinormal spectra of the solution are obtained applying two different methods and good convergence between both is achieved. Using the characteristic integration technique we tested the geometry evidencing its stability against linear scalar perturbations. As a consequence a two pattern set of frequencies (families) emerges, one oscillatory and another purely imaginary. In that spectra, the fundamental modes without angular momentum are hugely affected by the presence of the black hole charge surprisedly even for small values of this. Their evolution are controlled by purely imaginary frequencies as in the non-rotating chargeless BTZ case. Similar to others AdS black holes, the fundamental oscillations scale the black hole event horizon and the temperature of the hole (far from maximal charges).

Fisher information of a black hole spacetime

Relativistic quantum metrology is the study of optimal measurement procedures within systems that have both quantum and relativistic components. Here we use Unruh-DeWitt detectors coupled to a massless scalar field as probes of thermal parameters in different spacetimes via a relativistic quantum metrology analysis. We consider both (2 + 1)-dimensional anti-de Sitter and BTZ black hole spacetimes. We compute the Fisher information to identify characteristics of the black hole spacetime and to compare it to a uniformly accelerating detector in anti-de Sitter space. We find the dependence of the Fisher information on temperature, detector energy gap, black hole mass, interaction time, and the initial state of the detector. We identify strategies that maximize the Fisher information and therefore the precision of estimation.

Boosting thermodynamic performance by bending space-time

Black holes are arguably the most extreme regions of the universe. Yet, they are also utterly inaccessible to experimentation, and even just indirect observation poses significant technical challenges. The phenomenological approach of thermodynamics is uniquely suited to explore at least some of the physical properties of such scenarios, and this has motivated the study of so-called holographic engines. We show that the efficiency of an endoreversible Brayton cycle is given by the Curzon-Ahlborn efficiency, if the engine is fueled by a 2-dimensional ideal gas; and that the efficiency is higher, if the working medium is a (2 + 1)-dimensional BTZ black hole. These findings may be relevant not only in the quest to unlock the mysteries of black holes, but also for potential technological applications of graphene.

Thermodynamic quasi-stability of super entropic BTZ black hole

We know that criteria for thermodynamic stability of a most general black hole appears in the form of a series of inequalities connecting second-order derivatives of the black hole mass with respect to its parameters. Quasi-stable black holes satisfy some of these stability criteria in a certain regime of parameter space, but they never satisfy all the criteria simultaneously. We also know that specific heat, by virtue of our general stability criteria, is not necessarily negative for quasi-stable black holes. We show here that ([Formula: see text])-dimensional charged super entropic BTZ black hole is thermodynamically quasi-stable if fluctuation in cosmological constant is taken into account. We in fact study the fluctuations of all the thermodynamic parameters of this black hole in detail, namely, its charge, horizon area and cosmological constant. This detailed study concludes that this BTZ black hole transforms into some other kind of black hole during its Hawking decay and becomes stable. We also show differences in thermodynamic properties between this charged super entropic BTZ black hole and other AdS black holes.

Page curve for entanglement negativity through geometric evaporation

We compute the entanglement negativity for various pure and mixed state configurations in a bath coupled to an evaporating two dimensional non-extremal Jackiw-Teitelboim (JT) black hole obtained through the partial dimensional reduction of a three dimensional BTZ black hole. Our results exactly reproduce the analogues of the Page curve for the entanglement negativity which were recently determined through diagrammatic technique developed in the context of random matrix theory.

Geodesics and bending of light around a BTZ black hole surrounded by quintessential matter

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.

Stability analysis of circular orbits around a charged BTZ black hole spacetime in a nonlinear electrodynamics model via Lyapunov exponents

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 [Formula: see text] and coordinate time Lyapunov exponent [Formula: see text] are useful to determine the stability of these circular orbits. We observe the behavior of the ratio [Formula: see text] 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 [Formula: see text] as there is no proper time for massless test particles. More specifically, we further analyze the behavior of the ratio of [Formula: see text] to angular frequency [Formula: see text], so-called instability exponent as a function of charge [Formula: see text] and parameter related to cosmological constant [Formula: see text] for the particular values of other parameters.

Motion of particles and gravitational lensing around the (2+1)-dimensional BTZ black hole in Gauss\u2013Bonnet gravity

We study the motion of test particles and photons in the vicinity of the (2+1)-dimensional Gauss–Bonnet (GB) BTZ black hole. We find that the presence of the coupling constant serves as an attractive gravitational charge, shifting the innermost stable circular orbits outward with respect to the one for this theory in four dimensions. Further, we consider the gravitational lensing, to test the GB gravity in (2+1) dimensions and show that the presence of the GB parameter causes the bending angle to first increase with the increase in the inverse of the closest approach distance, u_0, reaching a peak value for a specific u_0^*, and then decreasing to zero. We also show that the increase in the value of the GB parameter decreases the bending angle, and the increase in the absolute value of the negative cosmological constant produces an opposite effect on this angle.

A correction of (2+1) Dimensional BTZ Black Hole Entropy as a New Series with Dependence on Plank Constant

We investigate the corrected entropy and Hawking temperature of the BTZ black hole which obtained from (2 + 1) dimensional black hole. Besides, we generalize our analysis of black holes to the case of Friedmann-Robertson-Walker (FRW) universe. The corrections to the Hawking temperature and entropy of apparent horizon for FRW universe are also obtained. Comparing the results with the high energy black hole demonstrates how the semi-classic approximation affects the thermodynamics of the BTZ black hole, corrected terms, classical action and the entropy.

Study of geodesic motion in a (2+1)-dimensional charged BTZ black hole

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.

Classical and quantum equations of motion of an n -dimensional BTZ black hole

We investigate the gravitational collapse of a non-rotating $n$-dimensional BTZ black hole in AdS space in the context of both classical and quantum mechanics. This is done by first deriving the conserved mass of a "spherically" symmetric domain wall, which is taken as the classical Hamiltonian of the black hole. Upon deriving the conserved mass, we also point out that, for a "spherically" symmetric shell, there is an easy and straight-forward way of determining the conserved mass, which is related to the proper time derivative of the interior and exterior times. This method for determining the conserved mass is generic to any situation (i.e. any equation of state), since it only depends on the energy per unit area, $\sigma$, of the shell. Classically, we show that the time taken for gravitational collapse follows that of the typical formation of a black hole via gravitational collapse, that is, an asymptotic observer will see that the collapse takes an infinite amount of time to occur, while an infalling observer will see the collapse to both the horizon and the classical singularity occur in a finite amount of time. Quantum mechanically, we take primary interest in the behavior of the collapse near the horizon and near the classical singularity from the point of view of both asymptotic and infalling observers. In the absence of radiation and fluctuations of the metric, quantum effects near the horizon do not change the classical conclusions for an asymptotic observer. The most interesting quantum mechanical effect comes in when investigating near the classical singularity. Here, we find, that the quantum effects in this region are able to remove the classical singularity at the origin, since the wave function is non-singular, and is also displays non-local effects, which depend on the energy density of the domain wall.

Accretion of dark energy onto higher dimensional charged BTZ black hole

In this work, we have studied the accretion of $(n+2)$-dimensional charged BTZ black hole (BH). The critical point and square speed of sound have been obtained. The mass of the BTZ BH has been calculated and we have observed that the mass of the BTZ BH is related with square root of the energy density of dark energy which accretes onto BH in our accelerating FRW universe. We have assumed modified Chaplygin gas (MCG) as a candidate of dark energy which accretes onto BH and we have found the expression of BTZ BH mass. Since in our solution of MCG, this model generates only quintessence dark energy (not phantom) and so BTZ BH mass increases during the whole evolution of the accelerating universe. Next we have assumed 5 kinds of parametrizations of well known dark energy models. These models generate both quintessence and phantom scenarios i.e., phantom crossing models. So if these dark energies accrete onto the BTZ BH, then in quintessence stage, BH mass increases upto a certain value (finite value) and then decreases to a certain finite value for phantom stage during whole evolution of the universe. We have shown these results graphically.

Holography of the BTZ black hole, inside and out

We propose a 1+1 dimensional CFT dual structure for quantum gravity and matter on the extended 2+1 dimensional BTZ black hole, realized as a quotient of the Poincare patch of AdS$_3$. The quotient spacetime includes regions beyond the singularity, "whiskers", containing timelike and lightlike closed curves, which at first sight seem unphysical. The spacetime includes the usual AdS-asymptotic boundaries outside the horizons as well as boundary components inside the whiskers. We show that local boundary correlators with some endpoints in the whisker regions: (i) are a protected class of amplitudes, dominated by effective field theory even when the associated Witten diagrams appear to traverse the singularity, (ii) describe well-defined diffeomorphism-invariant quantum gravity amplitudes in BTZ, (iii) sharply probe some of the physics inside the horizon but outside the singularity, and (iv) are equivalent to correlators of specific non-local CFT operators in the standard thermofield entangled state of two CFTs. In this sense, the whisker regions can be considered as purely auxiliary spacetimes in which these useful non-local CFT correlators can be rendered as local boundary correlators, and their diagnostic value more readily understood. Our results follow by first performing a novel reanalysis of the Rindler view of standard AdS/CFT duality on the Poincare patch of AdS, followed by exploiting the simple quotient structure of BTZ which turns the Rindler horizon into the BTZ black hole horizon. While most of our checks are within gravitational effective field theory, we arrive at a fully non-perturbative CFT proposal to probe the UV-sensitive approach to the singularity.

Quantum tunneling from generalized (2+1) dimensional black holes having Noether symmetry

We have studied the Hawking radiation from generalized rotating and static (2+1)-dimensional BTZ black holes. In this regard, we have benefited from the quantum tunneling approach with WKB approximation and obtained the tunneling rate of outgoing scalar and spinor particles across the horizons. We have also obtained the Hawking temperature at the horizons corresponding to the emission of these particles. It is shown that the tunneling rate and Hawking temperature of generalized (2+1)-dimensional BTZ black holes are different from ordinary (2+1)-dimensional BTZ black holes due to the Noether symmetry. In other words, the Noether symmetry can change the tunneling rate and Hawking temperature of the BTZ black holes. This symmetry may cause the BTZ black holes to avoid evaporation and its breakdown may start the evaporation.

Particle Collisions in the Lower Dimensional Rotating Black Hole Space-Time with the Cosmological Constant

We study the effect of ultrahigh energy collisions of two particles with different energies near the horizon of a2+1dimensional BTZ black hole (BSW effect). We find that the particle with the critical angular momentum could exist inside the outer horizon of the BTZ black hole regardless of the particle energy. Therefore, for the nonextremal 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 could only exist on the degenerated horizon, and the BSW process could also happen there.

Periodicity and area spectrum of the three dimensional BTZ black hole

Very recently, a new scheme to quantize the horizon area of a black hole has been proposed by Zeng and Liu et al. In this paper, we further apply the analysis to investigate area spectrum of three dimensional BTZ black hole with the cosmological constant \({\Lambda=-1/l^{2}}\) . The results show that the area spectrum and entropy spectrum are independent of the cosmological constant. The area spectrum of the black hole is \({\Delta A=8\pi l_{P}^{2}}\) , which confirms the initial proposal of Bekenstein that the area spectrum is independent of the black hole parameters and the spacing is \({8\pi l_{P}^{2}}\) . This result also confirms the speculation of Maggiore that the periodicity of a black hole may be the origin of the area quantization. In addition, for the rotating and non-rotating BTZ black holes, we obtain the same entropy spectrum \({\triangle S=2\pi}\) , which is consistent with the result for other black holes. This implies that the entropy spectrum is more fundamental than the area spectrum.

The energy-momentum tensor in the 1 + 1 dimensional non-rotating BTZ black hole

We study the energy-momentum tensor for the real scalar field on the 1+1 dimensional BTZ black hole. We obtain closed expressions for it.

Charged BTZ-like black holes in higher dimensions

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.

Quantum properties of the Dirac field on BTZ black hole backgrounds

We consider a Dirac field on a (1 + 2)-dimensional uncharged BTZ black hole background. We first find out the Dirac Hamiltonian, and study its self-adjointness properties. We find that, in analogy to the Kerr–Newman–AdS Dirac Hamiltonian in (1 + 3) dimensions, essential self-adjointness on C∞0(r+, ∞)2 of the reduced (radial) Hamiltonian is implemented only if a suitable relation between the mass μ of the Dirac field and the cosmological radius l holds true. The very presence of a boundary-like behaviour of r = ∞ is at the root of this problem. Also, we determine in a complete way the qualitative spectral properties for the non-extremal case, for which we can infer the absence of quantum bound states for the Dirac field. Next, we investigate the possibility of a quantum loss of angular momentum for the (1 + 2)-dimensional uncharged BTZ black hole. Unlike the corresponding stationary four-dimensional solutions, the formal treatment of the level crossing mechanism is much simpler. We find that, even in the extremal case, no level crossing takes place. Therefore, no quantum loss of angular momentum via particle pair production is allowed.

Eigenvalue Problem of Scalar Fields in BTZ Black Hole Spacetime

We studied the eigenvalue problem of scalar fields in the (2+1)-dimensional BTZ black hole spacetime. The Dirichlet boundary condition at infinity and the Dirichlet or the Neumann boundary condition at the horizon are imposed. Eigenvalues for normal modes are characterized by the principal quantum number (0 ≤ n) and the azimuthal quantum number (−∞ < m < ∞). Effects to eigenvalues of the black hole rotation and of the scalar field mass are studied explicitly. Relation of the black hole rotation to the super-radiant instability is discussed.