P-V Criticality of Modified BTZ Black Hole

In this paper, we investigate the BTZ black hole in P-V critical point of view. As we know, the BTZ black hole does not have P-V critical behavior. So in this case, we introduce some anstaz that give us the modified BTZ black hole. Finally, we show that this modified BTZ black hole is satisfied by the equation of state of Liquid-gas phase transition.     

Higher Order Quantum Corrections of Rotating BTZ Black Hole

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 picture of rotating BTZ black hole.     

Weak cosmic censorship conjecture in BTZ black holes with scalar fields

The weak cosmic censorship conjecture in the near-extremal BTZ black hole has been tested using test particles and fields.It has been claimed that such a black hole can be overspun.In this paper,we review the thermodynamics and weak cosmic censorship conjecture in BTZ black holes using the scattering of a 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 entropy,we test the weak cosmic censorship conjecture by evaluating the minimum of the function f,and find that both the extremal and near-extremal black holes cannot be overspun.     

Quantum correction to the entropy of noncommutative BTZ black hole

In this paper we consider the generalized uncertainty principle (GUP) in the tunneling formalism via Hamilton–Jacobi method to determine the quantum-corrected Hawking temperature and entropy for noncommutative BTZ black hole. In our results we obtain several types of corrections including the expected logarithmic correction to the area entropy associated with the noncommutative BTZ black holes. We also show that the area entropy product of the noncommutative BTZ black holes is dependent on mass and by analyzing the nature of the specific heat capacity we have observed that the noncommutative BTZ black hole is stable at some range of parameters.     

Entropy function approach to charged BTZ black hole

We find solution to the metric function f(r) = 0 of charged BTZ black hole making use of the Lambert function. The condition of extremal charged BTZ black hole is determined by a non-linear relation of M _e (Q) = Q ²(1 − ln Q ²). Then, we study the entropy of extremal charged BTZ black hole using the entropy function approach. It is shown that this formalism works with a proper normalization of charge Q for charged BTZ black hole because AdS₂ × S¹ represents near-horizon geometry of the extremal charged BTZ black hole. Finally, we introduce the Wald’s Noether formalism to reproduce the entropy of the extremal charged BTZ black hole without normalization when using the dilaton gravity approach.     

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.     

Three-dimensional massive Kiselev AdS black hole and its thermodynamics

We present an exact three-dimensional massive Kiselev AdS black hole solution. This Kiselev black hole is neither perfectly fluid, nor is it the quintessential solution, but the BTZ black hole modified by the anisotropic matter. This black hole possesses an essential singularity at its radial origin and a single horizon whose radius will increase monotonically when the parameter of the anisotropic matter field ω decreases. We calculate all thermodynamic quantities and find that the first law of thermodynamics of this massive Kiselev AdS black hole can be protected, while the consistent Smarr formula is only held in the extended thermodynamic phase space. After examining the sign of free energy, we conclude that there is no Hawking-Page transition since the massive Kiselev AdS black hole phase is always thermodynamically favored. Moreover, we study the phase transition between the Kiselev AdS black hole and BTZ black hole by considering the matchings for their temperature. We find that the Kiselev AdS black hole is still a thermodynamically more preferred phase, because it always has a smaller amount of free energy than the BTZ black hole, which seems to indicate that the anisotropic matter field may emerge naturally in BTZ black hole spacetime under some thermal fluctuations. We also show a first order phase transition between the Kiselev AdS black hole phase with -1w -1/2 and the black hole phase with -1/2w0. As the Kiselev AdS black hole has some notable features on the phase transition of black holes in three dimensions, it provides important clues to further investigate these both surprising and similar behaviors in four and higher dimensions.     

Cosmic string in the BTZ black hole background with time-dependent tension

In this Letter, we study the equation of circular loops with time-dependent tension in the BTZ black hole background. We obtain various cases where cosmic string loops finally collapse to form black holes. Also, we study effect of the BTZ black hole mass and angular momentum on the evolution of cosmic string loops. We find the critical values of initial radii as a limit for the cosmic string loops collapsing to form black holes.     

BTZ Black Hole in Non-Commutative Spaces

In this letter we compute the corrections to the horizons, the horizon area and Hawking temperature of a BTZ black hole. These corrections stem from the space non-commutativity. We show that in non-commutative case, non-rotating BTZ black hole in contrast with commutative case has two horizons.     

广义测不准关系与三维BTZ黑洞熵

通过应用在量子引力中,由广义测不准关系得出的新的态密度方程,研究三维BTZ背景下黑洞的熵.当取广义测不准关系中引入的,具有Planck量级与空间维数有关的常数λ为特定值时,得到BTZ黑洞Bekenstein-Hawking 熵和修正项.由于利用新的态密度方程,在计算中不存在用brick-wall模型计算黑洞熵时出现的发散项和小质量近似.所得结论,从量子统计力学角度给出了黑洞Bekenstein-Hawking 熵的修正值,使人们对黑洞熵的修正值有更深入的认识. 关键词： 广义测不准关系 量子统计 BTZ黑洞熵     

Generalized second law of thermodynamics for a phantom energy accreting BTZ black hole

In this paper, we have studied the accretion of phantom energy on a (2 + 1)-dimensional stationary Banados–Teitelboim–Zanelli (BTZ) black hole. It has already been shown by Babichev et al. that for the accretion of phantom energy onto a Schwarzschild black hole, the mass of black hole would decrease and the rate of change of mass would be dependent on the mass of the black hole. However, in the case of (2 + 1)-dimensional BTZ black hole, the mass evolution due to phantom accretion is independent of the mass of the black hole and is dependent only on the pressure and density of the phantom energy. We also study the generalized second law of thermodynamics at the event horizon and construct a condition that puts an lower bound on the pressure of the phantom energy.     

BTZ black holes in massive gravity

We analyze certain aspects of BTZ black holes in massive theory of gravity. The black hole solution is obtained by using the Vainshtein and dRGT mechanism, which is asymptotically AdS with an electric charge. We study the Hawking radiation using the tunneling formalism as well as analyze the black hole chemistry for such system. Subsequently, we use the thermodynamic pressure-volume diagram to explore the efficiency of the Carnot heat engine for this system. Some of the important features arising from our solution include the non-existence of quantum effects, critical Van der Walls behaviour, thermal fluctuations and instabilities. Moreover, our solution violates the Reverse Isoperimetric Inequality and, thus, the black hole is super-entropic, perhaps which turns out to be the most interesting characteristics of the BTZ black hole in massive gravity.     

W-hairs of the black holes in three-dimensional spacetime

In a previous publication, we claimed that a black hole can be considered as a topological insulator. A direct consequence of this claim is that their symmetries should be related. In this paper, we give a representation of the near-horizon symmetry algebra of the BTZ black hole using the W1+∞ symmetry algebra of the topological insulator in three-dimensional spacetime. Based on the W1+∞ algebra, we count the number of the microstates of the BTZ black holes and obtain the Bekenstein-Hawking entropy.     

Stability of the massive graviton around a BTZ black hole in three dimensions

We investigate the massive graviton stability of the BTZ black hole obtained from three dimensional massive gravities which are classified into the parity-even and parity-odd gravity theories. In the parity-even gravity theory, we perform the $s$ -mode stability analysis by using the BTZ black string perturbations, which gives two Schrödinger equations with frequency-dependent potentials. The $s$ -mode stability is consistent with the generalized Breitenlohner-Freedman bound for spin-2 field. It seems that for the parity-odd massive gravity theory, the BTZ black hole is stable when the imaginary part of quasinormal frequencies of massive graviton is negative. However, this condition is not consistent with the $s$ -mode stability based on the second-order equation obtained after squaring the first-order equation. Finally, we explore the black hole stability connection between the parity-odd and parity-even massive gravity theories.     

Charged BTZ-like black holes in higher dimensions

Motivated by many worthwhile papers about (2+1)-dimensional BTZ black hole solutions, we generalize them to (n+1)-dimensional solutions, the so-called BTZ-like solutions. We show that the electric field of BTZ-like solutions is the same as that of (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 obtain the conserved and thermodynamic quantities, and we show that they satisfy the first law of thermodynamics. Next, we perform a thermodynamic stability analysis in the canonical ensemble and find that the BTZ-like solutions are stable in the whole phase space.     

Holographic Entanglement Entropy of the BTZ Black Hole

We investigate quantum entanglement of gravitational configurations in 3D AdS gravity using the AdS/CFT correspondence. We derive explicit formulas for the holographic entanglement entropy (EE) of the BTZ black hole, conical singularities and regularized AdS₃. The leading term in the large temperature expansion of the holographic EE of the BTZ black hole reproduces exactly its Bekenstein-Hawking entropy S _BH , whereas the subleading term behaves as ln S _BH . We also show that the leading term of the holographic EE for the BTZ black hole can be obtained from the large temperature expansion of the partition function of a broad class of 2D CFTs on the torus. This result indicates that black hole EE is not a fundamental feature of the underlying theory of quantum gravity but emerges when the semiclassical notion of spacetime geometry is used to describe the black hole.     

Regular black hole in three dimensions

We find a new black hole in three-dimensional anti-de Sitter space by introducing an anisotropic perfect fluid inspired by the noncommutative black hole. This is a regular black hole with two horizons. We compare the thermodynamics of this black hole with that of a non-rotating BTZ black hole. The first-law of thermodynamics is not compatible with the Bekenstein–Hawking entropy.     

Scalar field in massive BTZ black hole and entanglement entropy

In this paper,we investigate the quantum scalar fields in a massive BTZ black hole background.We study the entropy of the system by evaluating the entanglement entropy using a discretized approach.Specifically,we fit the results with a log-modified formula of the black hole entropy,which is introduced by quantum correction.The coefficients of leading and sub-leading terms affected by the mass of graviton are numerically analyzed.     

Global geometry of the 2+1 rotating black hole

The generic rotating BTZ black hole, obtained by identifications in AdS₃ space through a discrete subgroup of its isometry group, is investigated within a Lie theoretical context. This space is found to admit a foliation by two-dimensional leaves, orbits of a two-parameter subgroup of and invariant under the BTZ identification subgroup. A global expression for the metric is derived, allowing a better understanding of the causal structure of the black hole.