Banados-Teitelboim-Zanelli Black Hole Research Articles

Noether symmetries, conservation laws and geometric properties of the Banados-Teitelboim-Zanelli black hole metric

This study provides a comprehensive analysis of the Banados-Teitelboim-Zanelli (BTZ) black hole, a significant solution in three-dimensional gravity. We begin with a detailed exploration of the BTZ black hole metric, highlighting its derivation and physical properties, such as its horizon structure and thermodynamic characteristics. The thermodynamics of BTZ black holes, including temperature, entropy, and free energy, are analyzed to understand their stability and behavior. A central focus of this work is the application of Noether symmetry principles to the BTZ black hole. We systematically compute the Noether symmetries of the BTZ metric and discuss their physical implications, including their role in conservation laws and stability analysis. This includes an examination of perturbations and their impact on the stability of the black hole, as well as a detailed geodesic analysis that leverages Noether symmetries to simplify the study of particle motion in this spacetime. Additionally, we investigate the first integrals associated with the BTZ black hole metric, elucidating their significance for the dynamics and conservation laws within this framework. The geometric analysis is further expanded through the Cartan structure equations, providing insight into the intrinsic geometric properties of the BTZ black hole and associated curvature tensors. Overall, this work integrates thermodynamic, symmetric, and geometric analyses to offer a unified understanding of the BTZ black hole’s structure and behavior, contributing to the broader field of black hole physics in lower-dimensional spacetimes.

BTZ black hole in [formula omitted] gravity and thermodynamic properties

In this study, we aim to investigate the rotating Banados-Teitelboim-Zanelli (BTZ) black hole (BH) solution within the framework of modified gravity theories. Notably, our investigation reveals that the BTZ BH space–time serves as a solution within the framework of Ricci-inverse (RI) gravity, particularly within Class-I models defined by f(R,A)=(R+αA). Here, R=gμνRμν and A=gμνAμν denote the Ricci and anti-curvature scalars, respectively, while α represents the coupling parameter. We show that this new modified theory induces modifications to the cosmological constant, demonstrating the influence of the coupling parameter α when analyzed in a vacuum as matter content. Additionally, we study the thermodynamic properties of this BTZ BH solution obtained within the RI-gravity framework and analyze the associated physical quantities. It is evident that the thermodynamic parameters, including BH horizons, Hawking temperature, entropy, free energy, internal energy, and specific heat capacity, undergo alterations due to the coupling constant α. Specifically, when α=0, our findings align with the outcomes documented in existing literature obtained in the general relativity (GR) context using the BTZ BH solution.

Quasibound states for a scalar field under the influence of an external magnetic field in the near-horizon geometry of the BTZ black hole with torsion

We consider a charged scalar field under the effect of an external uniform magnetic field in the near horizon of the Banados–Teitelboim–Zanelli black hole with torsion. By solving the corresponding Klein–Gordon equation, we determine quasi-stationary states of the system in question. We observe that the real and damped oscillations of the system depend on the strength of the external magnetic field as well as the parameters of the spacetime background. We see that the magnitude of the real oscillations decreases and the decay time of the damped modes becomes longer as the strength of the external magnetic field increases. Additionally, the results indicate that the background is stable under such a perturbation field.

On the curvature invariants of the massive Banados–Teitelboim–Zanelli black holes and their holographic pictures

In this paper, the curvature structure of a ([Formula: see text])-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 space–times. 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 nonmassive gravity. In addition, for the case of massive ([Formula: see text])-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 space–times. 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.

Weak cosmic censorship conjecture for the (2+1)-dimensional charged BTZ black hole in the Einstein–Gauss–Bonnet Gravity

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 show that the minimum energy that particle can have at the horizon becomes negative for both an extremal and nearly-extremal BTZ black holes in EGB gravity. It is proven that both extremal and nearly-extremal (2+1) dimensional BTZ black hole could be overcharged in EGB theory, leading to the violation of the weak cosmic censorship conjecture (WCCC), which is in good agreement with the results obtained for the classical BTZ black hole.

Entropy variation of rotating BTZ black hole under Hawking radiation

An axially symmetric rotating Banados-Teitelboim-Zanelli (BTZ) black hole is considered for comprehending its interior information. The largest space-like hyper-surface is chosen to estimate its maximal interior volume as a time-dependent quantity. Similarly, the quantum mode entropy of the scalar field associated with this volume is found to increase with Eddington time. An evolution relation between the variation of quantum mode entropy and Bekenstein-Hawking entropy is obtained for an infinitesimal time interval. On comparing to higher-dimensional black holes, the characteristic feature of this evolution relation is its divergent character.

Entanglement amplification from rotating black holes

The quantum vacuum has long been known to be characterized by field correlations between spacetime points. We show that such correlations—vacuum entanglement—in the environment of near-extremal black holes is significantly amplified (up to ten-fold) relative to their slowly rotating counterparts. We demonstrate this effect for rotating Banados–Teitelboim–Zanelli black holes by measuring the entanglement through the concurrence extracted from the vacuum via two-level quantum systems (Unruh–DeWitt detectors). The effect is manifest at intermediate distances from the horizon, and is most pronounced for near-extremal small mass black holes. The effect is also robust, holding for all boundary conditions of the field and at large spacelike detector separations. Smaller amplification occurs near the horizon, where we find that the entanglement shadow—a region near the black hole from which entanglement cannot be extracted—is diminished in size as the black hole’s angular momentum increases.

Fokker-Planck equation for black holes in thermal potential

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 spectrum is proportional to the temperature of the ensemble, which is an external parameter, and the ground state is non-zero. For BTZ black hole, the energy spectrum only depends on the AdS radius, which is the intrinsic parameter. Moreover, the ground state of BTZ black hole in thermal potential is zero. This also reflects the difference between three-dimensional gravity and four-dimensional gravity.

Collisional Penrose process of BTZ black holes

The Penrose process in the vicinity of an extremal Ban\~ados-Teitelboim-Zanelli(BTZ) black hole is studied. Due to the existence of negative cosmological constant, only massless particles could escape to infinity. Hence we analyse the Penrose process by one massless particle collides with another massive particle near the horizon of BTZ black holes. Calculations of the maximum energy extraction efficiency of this process is carried out for both spinless and spinning particles. Our results show that the spinning particle have a higher energy extraction efficiency than the spinless particle. Moreover, our calculation also indicates that the maximum energy extraction efficiency is independent of the value of the cosmological constant of BTZ black holes.

Scalar perturbations of black holes in Jackiw-Teitelboim gravity

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-Nordstr\"om 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 Ba\~nados-Teitelboim-Zanelli (BTZ) black hole and obtain the exterior and interior quasinormal modes. The dynamics of a scalar field near the Cauchy horizon mimics the behavior of the same for the usual BTZ black hole, indicating a possible violation of the strong cosmic censorship conjecture in the near extreme limit. However, quantum effects seem to rescue strong cosmic censorship.

Rotating and charged Gauss–Bonnet BTZ black holes

We obtain charged and rotating black hole solutions to the novel 3D Gauss–Bonnet theory of gravity recently proposed, both of which generalize the Banados–Teitelboim–Zanelli (BTZ) metric. The charged solutions are obtained in the Maxwell and Born–Infeld theories and feature ‘universal thermodynamics’—identical to the thermodynamics of their Einstein cousins. The rotating Gauss–Bonnet BTZ black holes are quite exceptional 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. Extending our considerations to higher dimensions, we also obtain novel 4D Gauss–Bonnet rotating black strings.

Event horizon detecting invariants

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 Ba\~nados-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 dimensional Kerr, five dimensional Myers-Perry and three dimensional warped-anti--de Sitter, and the three dimensional asymptotically flat black holes as examples.

Entropy Variation of a Charged (2 + 1)-Dimensional BTZ Black Hole Under Hawking Radiation

Using the definition of a black hole’s volume introduced by Christodoulou and Rovelli, we calculate the interior volume of a (2 + 1)-dimensional charged Banados Teitelboim Zanelli (BTZ) black hole, and find that the volume increases linearly with time. Afterwards, the entropy of a massless scalar field inside the black hole is calculated and the result indicates that the entropy will be also increasing with time infinitely. Moreover, thinking about Hawking radiation, the ratio of variation of the scalar field’s entropy to the variation of Bekenstein–Hawking entropy is approximately a linear function of m, which is quite different from a RN black hole while m is relatively large. In the end, we extend the calculation above to a massive BTZ black hole and find that the relationship with different $\tilde {M}$ between two kinds of entropy is similar to the previous result. But the difference is that the relationship function $F(m,q,\tilde {M})$ will tend to be a constant when the mass parameter $\tilde {M}$ becomes big enough.

BTZ black hole with Korteweg–de Vries-type boundary conditions: Thermodynamics revisited

The thermodynamic properties of the Ba\~nados-Teitelboim-Zanelli (BTZ) black hole endowed with Korteweg-de Vries (KdV)-type boundary conditions are considered. This familiy of boundary conditions for General Relativity on AdS$_{3}$ is labeled by a non-negative integer $n$, and gives rise to a dual theory which possesses anisotropic Lifshitz scaling invariance with dynamical exponent $z=2n+1$. We show that from the scale invariance of the action for stationary and circularly symmetric spacetimes, an anisotropic version of the Smarr relation arises, and we prove that it is totally consistent with the previously reported anisotropic Cardy formula. The set of KdV-type boundary conditions defines an unconventional thermodynamic ensemble, which leads to a generalized description of the thermal stability of the system. Finally, we show that at the self-dual temperature $T_{s}= \frac{1}{2\pi}(\frac{1}{z})^{\frac{z}{z+1}}$, there is a Hawking-Page phase transition between the BTZ black hole and thermal AdS$_{3}$ spacetime.

Non-Einsteinian black holes in generic 3D gravity theories

The Ba\~nados-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.

Gedanken experiments to destroy a BTZ black hole

We consider Gedanken experiments to destroy an extremal or near-extremal Banados-Teitelboim-Zanelli (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 three-dimensional Einstein gravity and chiral gravity, which both live in the torsionless limits of the Mielke-Baekler model, an extremal BTZ black hole cannot be overspun; and (iii) in both Einstein gravity and chiral gravity, a near-extremal BTZ black hole cannot be overspun, leaving the weak cosmic censorship preserved. To obtain these results, we follow the analysis of Sorce and Wald on their Gedanken experiments to destroy a Kerr-Newman black hole, and calculate the second order variation of the black hole mechanics. Furthermore, Wald's type of Gedanken experiments provide an operational procedure of proving the third law of black hole dynamics. Through the $\mathrm{AdS}/\mathrm{CFT}$ correspondence, our results on BTZ black holes also indicate that a third law of thermodynamics holds for the holographic conformal field theories dual to three-dimensional Einstein gravity and chiral gravity.

Entropy relations and bounds of BTZ black hole in gravity's rainbow

In this paper, we present the entropy relations and bounds of Banados–Teitelboim–Zanelli (BTZ) black hole in two models of gravity's rainbow. Because of the effect of gravity's rainbow, one can find that the entropy product and sum both lost their universality and become mass-dependent. On the other hand, comparing the entropy bound of event horizon to the BTZ case, it is shown that the angular momentum [Formula: see text] enlarges the entropy bound while the gravity's rainbow parameter [Formula: see text] diminishes it. For the entropy bound of Cauchy horizon, the gravity's rainbow parameter [Formula: see text] enlarges it at the large [Formula: see text] limit, while [Formula: see text] diminishes it at the small [Formula: see text] limit. These suggest some clues on the geometrical origin of black hole entropy bounds.

Interior volume of Banados–Teitelboim–Zanelli black hole

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.

Quantum gravity effect on the Hawking radiation of charged rotating BTZ black hole

In this study, the quantum gravity effect on the tunnelling radiation of charged massive spin-0 scalar particle from 2+1 dimensional charged rotating Banados-Teitelboim-Zanelli (BTZ) black hole is looked into by using the Hamilton-Jacobi approach. For this, we calculate the modified Hawking temperature of the black hole by using the modified Klein-Gordon equation based on the Generalized Uncertainty Principle (GUP), and we noticed that the modified Hawking temperature of the black hole depends not only on the black hole properties, but also on the angular momentum, energy, charge and mass of the tunnelling scalar particle. Using the modified Hawking temperature, we discussed the stability of the black hole in the context of the modified heat capacity, and observed that it might undergo both first and second-type phase transitions in the presence of the quantum gravity effect, but just a first-type transition in the absence of the quantum gravity effect. Furthermore, we investigated the modified Hawking temperature of the black hole by using the tunnelling processes of the charged massive Dirac and vector boson particles. We observed that scalar, Dirac and vector particles are tunnelled from the black hole completely differently from each other in the presence of the quantum gravity effect.

Beyond anyons

The theory of anyon systems, as modular functors topologically and unitary modular tensor categories algebraically, is mature. To go beyond anyons, our first step is the interplay of anyons with conventional group symmetry due to the paramount importance of group symmetry in physics. This led to the theory of symmetry-enriched topological order. Another direction is the boundary physics of topological phases, both gapless as in the fractional quantum Hall physics and gapped as in the toric code. A more speculative and interesting direction is the study of Banados–Teitelboim–Zanelli (BTZ) black holes and quantum gravity in 3d. The clearly defined physical and mathematical issues require a far-reaching generalization of anyons and seem to be within reach. In this short survey, I will first cover the extensions of anyon theory to symmetry defects and gapped boundaries. Then, I will discuss a desired generalization of anyons to anyon-like objects — the BTZ black holes — in 3d quantum gravity.