M. A. Anacleto, F. A. Brito, E. Passos, Jose L. Paulino, A. T. N. Silva, J. Spinelly
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.
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In this paper, we study the Hawking temperature of the BTZ black hole based on the purely topological method proposed by Robson, Villari, and Biancalana (RVB) [Phys. Rev. D 99, 044042 (2019)]. The Hawking temperature of the charged rotating BTZ black hole can be accurately derived by this topological method. We also calculate the Hawking temperature of the BTZ black hole in massive gravity. Because the metric function of the BTZ black hole in massive gravity has a mass term, the corresponding Hawking temperature cannot be derived unless an integral constant is added.
Semiclassical Corrections to the Bekenstein-Hawking entropy of the BTZ Black Hole via Self-Gravitation
霍金辐射被看作是一个隧穿过程。这样，自引力效应引起对（2+1）BTZ黑洞熵的半经典修正。由于自引力效应的特定模型，（2+1）BTZ黑洞的修正熵进行了评估。对于BTZ黑洞事件视界外辐射的能量壳层$ω$，修正熵与视界成正比。在这个半经典分析中，对贝肯斯坦-霍金公式$S_{BH}=\mathcal{A}_{H} / 4l_{P}^{2}$的修正被发现是负的，并且将（2+1）BTZ黑洞的修正熵$S_{bh}$与贝肯斯坦-霍金熵$S_{BH}$联系起来的比例因子在$ω$中被估计为一阶。
Remarks on Hawking radiation as tunneling from the BTZ black holes
在考虑发射粒子的自引力效应的情况下，不仅考虑能量守恒，而且考虑角动量守恒，重新研究了（2 + 1）维旋转BTZ黑洞事件视界的半经典隧穿过程霍金辐射.与文献中对这个问题的分析相反，我们的结果与Kraus-Parikh-Wilczek的普适结论吻合得很好，而不需要对BTZ黑洞的Bekenstein-Hawking面积熵公式作任何修改.
Logarithmic correction to the Bekenstein-Hawking entropy of the BTZ black hole
我们导出了欧几里德BTZ黑洞配分函数的精确表达式。利用这一结果，我们证明了对于具有大视界面积的黑洞，对Bekenstein-Hawking熵的修正是$-3/2 log(Area)$，这与Schwarzschild黑洞的正则引力形式和BTZ黑洞熵的Lorentz计算结果一致.我们发现，在BTZ黑洞的上下文中的对数校正的正确的表达式来自与黑洞的toral边界的模不变性。
Hawking temperature in the eternal BTZ black hole: an example of Holography in AdS spacetime
本文综述了1+2维AdS时空与BTZ黑洞的关系。后来，我们表明，在AdS时空的基态成为BTZ黑洞的热态。我们表明，这是真实的，在散装和边界的AdS时空。这种热态的存在等于说，Unruh效应存在于AdS时空中，并成为永恒BTZ黑洞的霍金效应。为了做到这一点，我们使用代数全息中引入的对应关系，分别与AdS时空及其共形边界中的楔形和双锥区域相关的准局部可观测量代数之间。我们还给出了实标量量子场作为这种形式的具体启发式实现。
We compute the transition rate of an Unruh-DeWitt detector coupled both to a ground state and to a KMS state of a massless, conformally coupled scalar field on a static BTZ black hole with Robin boundary conditions. We observe that, although the anti-Hawking effect is manifest for the ground state, this is not the case for the KMS state. In addition, we show that our analysis applies with minor modifications also to the anti-Unruh effect on Rindler-AdS$_3$ spacetime.
Hawking-Page phase transition in BTZ black hole revisited
我们考虑了$M \ge 0$的BTZ黑洞与$M=-1$的热孤子之间的Hawking-Page相变.在这个系统中，存在一个质量间隙，因此似乎不存在连续的热力学相变。通过适当考虑圆锥空间，我们一致地构造了黑洞和孤子的离壳自由能。然后，通过非平衡孤立子可以实现描述隧道效应的连续离壳自由能。
Gauge and Gravitational Anomalies and Hawking Radiation of Rotating BTZ Black Holes
本文从规范反常和引力反常的观点出发，得到了旋转BTZ黑洞的霍金辐射通量。然后，我们表明，在BTZ时空中的规范和引力异常被抵消的总通量的2维黑体在霍金温度的时空。
We re-examine Hawking radiation for a nonrotating (2+1)-dimensional 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.
The Unruh effect is a surprising prediction of quantum field theory that asserts accelerating observers perceive a thermal spectrum of particles with a temperature proportional to their acceleration. However, it has recently been shown that particle detectors can click less often or even cool down as their acceleration increases, in contrast to the heating one would expect. This leads to the so called anti-Unruh phenomena. Here we consider detectors outside a BTZ black hole and demonstrate the existence of black hole analogues of these effects, which we dub anti-Hawking phenomena.
Phase transitions of the BTZ black hole in new massive gravity
本文研究了新的大质量引力下BTZ黑洞的热力学性质。对于具有四阶项质量参数$m^2$和$\ell^2$ AdS $_3$曲率半径的$m^2\ell^2>1/2$，BTZ黑洞和AdS（热）孤子之间发生Hawking-Page相变.然而，对于$m^2\ell^2<1/2$，这种转变不太可能发生，但BTZ黑洞和无质量BTZ黑洞之间的相变可能发生。我们称后者为逆Hawking-Page相变，这种相变在新的大质量引力中是有利的。
Hawking radiation from (2+1)-dimensional BTZ black holes
基于Robinson-Wilczek最近提出的霍金辐射可以看作是抵消Schwarzschild型黑洞视界处引力异常所需的能量动量张量通量的观点，我们研究了旋转$(2+1)$维BTZ黑洞和带电$(2+1)$维BTZ黑洞通过抵消视界处的规范异常和引力异常所产生的霍金辐射.为了在量子水平上恢复规范不变性和广义坐标协变性，必须引入相应的规范流和能量动量张量通量，以抵消视界上的规范和引力异常。结果表明，这些补偿通量的值与霍金温度下的$(1+1)$维黑体辐射的值完全相等。
Hawking radiation as a quantum tunneling phenomena from accelerating BTZ black holes is presented in this work. We have calculated the Dirac particle's Hawking radiation from the horizon of the accelerating BTZ black hole. WKB approximation is applied to Dirac equation in the background of three dimensional black holes. This procedure gives us the tunneling probability, which we have used to calculate the Hawking temperature of the background three-dimensional black hole. Our study is consistent with the previous studies in the absence of the acceleration parameter. We have also studied the qu…
Quantum correlation and origin of Hawking radiation for mass-superposed BTZ black holes
利用速度关联函数研究BTZ黑洞质量叠加，发现关联峰可揭示量子特征并区分相同质量比的不同叠加，且能定位Hawking辐射起源，支持量子大气概念。
Entropy of BTZ black strings in the brick wall approach
在过去的几年中，精确的解决方案，描述黑洞是绑定到一个二维膜在一个四维anti-de Sitter散装已建成。在膜上有负宇宙学常数的情况下，对于大质量，这些解正好是膜上旋转的BTZ黑洞，事实上，描述了整体旋转的BTZ黑弦。本文利用brick wall模型计算了在霍金温度下，自由无质量标量场在旋转BTZ黑弦周围的正则熵。我们明确表明，贝肯斯坦-霍金的面积法是满足膜以及在散装。
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…
Thermodynamics of noncommutative BTZ black hole
研究了非对易几何中BTZ黑洞的热力学性质。当非对易性参数趋于零时，霍金温度和熵降到它们的对易极限。我们还讨论了在非对易情况下霍金面积定律的有效性范围，并提供了图形分析。我们看到，除非外视界非常大，否则定律是无效的。
Where are the BTZ Black Hole Degrees of Freedom? The Rotating Case
最近的工作表明，非旋转BTZ黑洞的熵可以从任何空间位置的对偶共形描述中导出。在这个后续行动中，它表明，一个双重的共形描述存在于任何空间位置的旋转BTZ黑洞以及。在非旋转的情况下，两个副本的中心荷$c^{\pm} = 3\ell/2G$恢复和微正则卡迪公式产生正确的贝肯斯坦-霍金熵。
BTZ Black Hole Entropy and the Turaev-Viro model
我们证明了从自旋泡沫模型和正则量子化的观点导出的欧几里德BTZ黑洞的Bekenstein-Hawking熵之间的一致性。这是通过考虑图拉夫-维罗状态和模型中的可观测图形（对应于黑洞视界），然后解析地将所得配分函数继续为宇宙学常数的负值来完成的。
No Hawking-Page phase transition in three dimensions
我们研究了霍金-佩奇相变是否可能在三维空间中发生。从最简单的一类Lanczos-Lovelock作用量开始，所有不带电的AdS型黑洞的热力学行为分为两类：偶数维的Schwarzschild-AdS黑洞和奇数维的Chern-Simons黑洞。前者可以提供Schwarzschild-AdS黑洞和热AdS空间之间的Hawking-Page跃迁。另一方面，后一类是例外的，因此Hawking-Page转变很难发生。在三维空间中，非旋转BTZ黑洞和无质量BTZ黑洞（热AdS空间）之间可能发生二阶相变，而非非旋转BTZ黑洞和热AdS空间之间的一阶Hawking-Page相变.
Hawking temperature of black holes with multiple horizons
本文研究多视界黑洞的有效霍金温度，分析四维旋转带电黑洞与旋转 BTZ 黑洞，指出各视界均有贡献，并比较其温度对质量及角动量的依赖。
Unruh-DeWitt detector on the BTZ black hole
本文在一阶微扰理论下研究了三维弯曲时空中与标量场耦合的Unruh-DeWitt粒子探测器。我们首先得到一个因果关系和明显的正则表达式的瞬时跃迁率在任意的阿达玛状态。然后，我们专门的Bañados-Teitelboim-Zanelli黑洞和一个无质量的共形耦合场的哈特尔-霍金真空。一个同向旋转的探测器在预期的局部霍金温度下产生热响应，而一个自由下落的探测器在我们能够探测的区域没有显示出热性的证据，甚至离视界不远。渐近反de Sitter无穷远处的边界条件对跃迁速率有显著影响。
We investigate the correlation harvesting protocol for mutual information between two Unruh-DeWitt detectors in a static BTZ black hole spacetime. Here, the effects coming from communication and change in proper separation of the detectors are set to be negligible so that only a black hole affects the extracted mutual information. We find that, unlike the entanglement harvesting scenario, harvested mutual information is zero only when a detector reaches an event horizon, and that although the Hawking effect and gravitational redshift both affect the extraction of mutual information, it is extr…
We derive the Hawking radiation spectrum of anyons, namely particles in (2+1)-dimension obeying fractional statistics, from a Bañados, Teitelboim, and Zanelli (BTZ) black hole, in the tunneling formalism. We examine ways of measuring the spectrum in experimentally realizable systems in the laboratory.
We present the thermodynamics of a charged and rotating BTZ black holes here. In particular, we derive expressions for various macroscopic thermal quantities such as entropy, Hawking temperature, Helmholtz free energy, internal energy, enthalpy, Gibbs free energy, and specific heat. To study the effects of small statistical thermal fluctuations around the equilibrium on thermodynamics, we calculated the leading-order corrections to the various thermodynamical potentials of charged and rotating BTZ black hole and do comparative analysis for the fixed values of charge and angular momentum.
Acceleration radiation and HBAR thermodynamics for atoms falling into a BTZ black hole: A CQM quantum-optics approach
研究落入BTZ黑洞的原子，利用量子光学方法，表明原子会发射霍金温度下的普朗克谱辐射，与相对等效原理有关，此辐射特性由近视界共形量子力学支配，还产生模仿贝肯斯坦 - 霍金熵的ħ熵。
Thin-shell gravastar model in a BTZ geometry with minimum length
本文在具有最小长度的BTZ几何中构建了两个球对称薄壳引力真空星模型，分别用二维氢原子基态概率密度和洛伦兹型分布引入最小长度效应，发现其能量密度和压力特征可使引力真空星稳定，并研究了薄壳熵及BTZ黑洞的热力学稳定性。
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 B…
Where are the BTZ Black Hole Degrees of Freedom?
先前从对偶共形描述推导出的BTZ黑洞熵，将自由度置于空间无穷远。在这里，它示出的非旋转的情况下，一个双保形描述存在于周围的黑洞，一个结果，具有很强的物理吸引力，考虑到在2+1维没有传播的自由度在经典理论中的任何位置。恢复了$3\ell/2G$中心荷的两个拷贝，微正则Cardy公式得到了正确的贝肯斯坦-霍金熵。
In this manuscript, we investigate the thermal properties of the rotating charged BTZ black hole under the gravity's rainbow (GR) and generalized uncertainty principle (GUP) formalism. At first, we study the GR-corrected thermal quantities according to the usual Heisenberg algebra. Then, we consider a deformed algebra that leads to a change in the Heisenberg uncertainty principle and compare the Hawking temperature, entropy, thermodynamical volume, pressure, and heat capacity functions with the previous results. Thus, we understand and interpret the quantum effects on the BTZ black hole.
In this paper, the tunneling of scalar particles near the event horizons of Riemann space time, BTZ black hole and Schwarzschild-de Sitter black hole are investigated by applying Hamilton-Jacobi equation with Lorentz violation theory in curved space time. The modified Hamilton-Jacobi equation is derived from Klein-Gordon equation of scalar particles induced by Lorentz violation theory in curved space time. The Hawking temperatures of Riemann space time and the BTZ black hole are modified due to the effect of Lorentz violation theory. Moreover, the Bekenstein-Hawking entropy near the event hori…
Entropy of BTZ black hole and its spectrum by quantum radial geodesics behind horizons
在完全限定在视界后的径向测地线的热量子化框架下，我们计算了BTZ黑洞的熵，其结果与Bekenstein-Hawking关系一致。BTZ黑洞中的粒子占据了唯一的量子基态。量子化使我们能够找到黑洞质量与其轨道动量的线性关系。
Statistical Entropy of BTZ Black Hole in Higher Curvature Gravity
对于BTZ黑洞，在Einstein引力下，我们计算了一个统计熵，它等于Bekenstein-Hawking熵.本文计算了高曲率引力下BTZ黑洞的统计熵，并证明了它与用Noether荷方法导出的统计熵相等。这表明，在一般的引力同形不变理论中，黑洞的几何熵和统计熵是等价的。讨论了宇宙监督猜想与AdS边界上共形场论的么正性之间的关系。
We investigate the effect of noncommutativity and quantum corrections to the temperature and entropy of a BTZ black hole based on a Lorentzian distribution with the generalized uncertainty principle (GUP). To determine the Hawking radiation in the tunneling formalism we apply the Hamilton-Jacobi method by using the Wentzel-Kramers-Brillouin (WKB) approach. In the present study we have obtained logarithmic corrections to entropy due to the effect of noncommutativity and GUP. We also address the issue concerning stability of the non-commutative BTZ black hole by investigating its modified specif…
Quasinormal Modes and GUP-Corrected Hawking Radiation of BTZ Black Holes within Modified Gravity Frameworks
本文在f(R)与Ricci-Inverse修正引力框架下研究BTZ黑洞的准正规模式和有效势，并结合广义不确定性原理分析其对黑洞辐射的影响，为通过引力波观测检验修正引力理论提供依据。
Exploring Quantum Corners: How Curved Momentum Space Shapes BTZ Black Holes
研究弯曲动量空间对BTZ黑洞的影响，通过(2 + 1)维框架，利用时空定位算符非对易代数重构动量空间几何，导出应力 - 能量张量，得到变形BTZ黑洞及相关修正，还研究了霍金辐射，为量子几何与黑洞物理搭建现象学桥梁。
Radiation via Tunneling in the Charged BTZ Black Hole
把霍金（黑洞）辐射看作是量子隧穿过程往往是方便的。在这个框架内，Kraus和Wilczek（KW）已经开始了黑洞发射的分析处理。值得注意的是，他们的方法结合了动态黑洞几何的影响。本文将KW形式应用于带电BTZ黑洞的情形。在这个有趣的模型的背景下，我们能够证明一个非热谱，与通常的霍金结果被复制在零阶频率。相当多的注意力，然后给予近极值热力学的检查。
Thermodynamics of rotating thin shells in the BTZ spacetime
本文研究旋转薄壳的热力学平衡态，一个环，在一个具有负宇宙学常数的（2+1）维时空中。相对于壳层的内部和外部区域分别由真空反德西特时空和旋转的巴尼亚多斯-泰特尔邦-扎内利时空给出。薄壳上的热力学热力学第一定律，连同三个状态方程的压力，当地的逆温度和热力学角速度的壳，产生壳的熵，这是只依赖于它的引力半径。当壳层被推到它自己的引力半径，并且它的温度取为相应黑洞的霍金温度时，壳层的熵与贝肯斯坦-霍金熵一致。此外，我们认为简单ansätze的状态方程，以及幂律状态方程的熵和热力学稳定性条件可以分析检查。
Quantum corrections for BTZ black hole via 2D reduced model
利用二维降维模型研究了BTZ黑洞的单圈量子修正。三维最小和保形耦合的情况下进行了分析。两种情况下被认为是：最小耦合和共形耦合三维标量物质。在极小情形下，定义了Hartle-Hawking和Unruh真空态，并求出了相应的几何半经典修正，同时对共形情形也进行了计算，以便与以前在无自旋黑洞的特殊情形下得到的精确结果进行比较.此外，我们还得到了AdS黑洞在二维最小耦合标量场的Hatrle-Hawking态和Boulware态下的精确修正
Horizon Dynamics of a BTZ Black Hole
在文献中已经提出，给定一个黑洞时空，相对论膜可以提供视界动力学的有效描述。在本文中，我们探讨了这样一个框架的背景下，一个2+1维BTZ黑洞。按照这个膜的规定，我们能够将视界动力学（现在用弦来描述）转化为1+1维克莱因-戈登方程的方便形式。我们继续计算这些解并构造热力学配分函数。最终，我们能够提取量子校正熵，这表明符合贝肯斯坦-霍金面积定律的BTZ形式。我们还证实，领先的顺序校正是成正比的对数的面积。
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, …
Microscopic entropy of the charged BTZ black hole
荷电BTZ黑洞的特征是由黑洞的电荷产生的幂律曲率奇异性。曲率奇异性在引力场的渐近展开中产生ln r项，并对边界项产生发散贡献。我们表明，这些边界变形可以产生的行动的共形群在两个维度和一个适当的重整化过程允许有限的边界电荷的定义。在半经典区域，对偶CFT的中心荷是由Brown和Henneaux计算的，而与时间平移相关的电荷是由重整化黑洞质量给出的。我们证明了Cardy公式精确地再现了带电BTZ黑洞的Bekenstein-Hawking熵。
Thermodynamics and thermal stability of BTZ-ModMax black holes
本文在ModMax非线性电动力学框架下构造了BTZ黑洞精确解，推导其热力学量及第一定律，并通过热容与自由能分析确定了同时满足局部和全局热稳定性的参数区域。
Exact Results for the BTZ Black Hole
本文综述了三维BTZ黑洞的精确结果。我们用严格的数学结果来阐明这个黑洞时空的一般结构和性质以及它的微观描述。特别是，我们研究了点粒子碰撞形成的黑洞，导致精确的分析确定的Choptuik标度参数。我们还表明，“无毛定理”如下立即从数学定理的双曲几何，由于沙利文。微观的理解的贝肯斯坦-霍金熵，和衰变率的无质量标量，遵循标准结果的共形场论。
Quantum thermodynamics in a rotating BTZ black hole spacetime
本文从量子热力学角度研究BTZ黑洞外UDW探测器的热化过程，利用多种信息论工具揭示其内禀不对称性，发现加热快于冷却的量子Mpemba效应，并证明黑洞自旋显著影响该不对称性的大小。
Two-dimensional Quantum Black Holes, Branes in BTZ and Holography
我们解决了半经典爱因斯坦方程在二维与一个巨大的源，我们发现一个静态的，量子稳定的，量子黑洞解在Hartle-Hawking真空状态。然后，我们研究的黑洞的几何形状所产生的边界质量坐在一个非零张力1-膜嵌入在一个三维BTZ黑洞。我们表明，这两种几何形状相吻合，我们提取，使用全息关系，信息的CFT生活在1-膜。最后，我们证明了量子黑洞具有与体BTZ相同的温度，正如全息原理所预期的那样。
The entropy formula of black holes in Minimal Massive Gravity and its application for BTZ black holes
本文用Tachikawa方法\cite{a}得到了最小质量引力（MMG）黑洞解的熵公式。然后我们将这个公式应用于BTZ黑洞解。我们发现通常的贝肯斯坦-霍金熵被修改。修正来自于Chern-Simons（CS）项和MMG中的新项。CS项的贡献与视界的内径成正比，这不是新的结果，而最后一项则是MMG项的贡献，它与视界的外径成正比，这是新的结果。然后证明了对偶边界连续傅里叶变换的熵的Cardy公式可以精确地再现总熵。
BTZ black holes are excellent laboratories for studying black hole thermodynamics which is a bridge between classical general relativity and quantum nature of gravitation. In addition, three-dimensional gravity could have equipped us for exploring some of the ideas behind the two dimensional conformal field theory based on the $AdS_{3}/CFT_{2}$. Considering the significant interests in these regards, we examine charged BTZ black holes. We consider the system contains massive gravity with energy dependent spacetime to enrich the results. In order to make high curvature (energy) BTZ black holes …
In this work, we study gravity duals of conformal field theories with boundaries known as AdS/BCFT correspondence, put forward by Takayanagi [1], within a scalar-tensor theory, as proposed by Horndeski in 4D [2]. We consider the case of 3D gravity dual to 2D BCFT, take a Gibbons-Hawking surface term modified by Horndeski's theory and find the corresponding 3D (BTZ) black hole solutions. We analyze the effects of Horndeski's gravity on the profile of the extra boundary for the black hole by using an approximate analytic solution. Performing a holographic renormalization, we have calculated the …
Two-Dimensional Dilatonic Black Holes and Hawking Radiation
从二维带电和不带电的双光子黑洞--分别从（2+1）自旋和无自旋的BTZ黑洞维化约--发出的霍金辐射被看作是一个隧穿过程。与计算霍金辐射时背景几何是固定的标准方法不同，二维电子黑洞（包括AdS（2））被视为动力学背景.这种几何形状的改变在辐射光谱中产生了非热部分。我们发现了极端二维带电黑洞的非零温度，并在这些动力学几何下，容易地导出了Bekenstein-Hawking面积公式。
Quantum Liouville theory and BTZ black hole entropy
本文给出了（2+1）维BTZ黑洞熵的共形场论描述。在边界Liouville场论中，我们研究了椭圆扇区中的可约Verma模，它对应于量子代数U_q（sl_2）\odot U_{ \hat{q} }（sl_2）的某些不可约表示。我表明，有状态，从这些可简化的Verma模块以类似的方式在极小模型的空状态的解耦。由于量子刘维场论中两点关联函数的沃德恒等式的非标准形式，这些退耦态具有正定范数。当q是奇数阶的单位根时，从这些状态的显式计数给出了半经典极限中所需的贝肯斯坦-霍金熵。
We investigate the stability of the inner horizon of a rotating BTZ black hole. We show that linear perturbations arising from smooth initial data are arbitrarily differentiable at the inner horizon if the black hole is sufficiently close to extremality. This is demonstrated for scalar fields, for massive Chern-Simons fields, for Proca fields, and for massive spin-2 fields. Thus the strong cosmic censorship conjecture is violated by a near-extremal BTZ black hole in a large class of theories. However, we show that a weaker "rough" version of the conjecture is respected. We calculate the renorm…
Scalar Fields in BTZ Black Hole Spacetime and Entanglement Entropy
研究了BTZ黑洞时空背景中的量子标量场。我们用离散化的模型计算了纠缠熵，该模型类似于耦合谐振子系统。熵公式的首项是标准Bakenstein-Hawking熵，次首项对应于对黑洞熵的量子修正。数值计算了次超前对数改正系数。
Correspondence between the contracted BTZ solution of cosmological topological massive gravity and two-dimensional Galilean conformal algebra
我们证明了宇宙拓扑质量引力（CTMG）的BTZ黑洞解具有隐共形对称性。在这方面，我们考虑了在BTZ时空中传播的无质量标量场的波动方程，发现波动方程可以用$SL(2,R)$二次Casimir表示。从共形坐标中，可以直接读取双CFTs的温度。此外，我们还利用Cardy公式计算了对偶CFT的微观熵，并找到了与BTZ黑洞的Bekenstein-Hawking熵的完美匹配。然后我们考虑了相对论性共形代数（$x\rightarrow εx$，$t\rightarrow t$，$ε\rightarrow 0$）的一种收缩形式--GCA.我们发现，有一个对应关系之间的$GCA_2$的边界和收缩BTZ的散装。为此，我们得到了$GCA_2$的中心荷和温度。然后利用Cardy公式计算了$GCA_2$的微观熵，并在非相对论极限下找到了与BTZ黑洞的Bekenstein-Hawking熵的完美匹配.近区标量场的吸收截面也与双$GCA_2$的微观吸收截面相匹配。从而进一步证明了收缩BTZ黑洞与二维伽利略共形代数之间的对应关系。
Chaos, Phase Transitions and Curvature Invariants of (rotating, warped, massive) BTZ Black Holes
本文综合研究BTZ及扭曲BTZ黑洞，利用有效温度、物理热力学系综和曲率不变量澄清混沌界饱和、相变行为及模置乱模式的几何对应。
On the thermal description of the BTZ black holes
我们研究了三维BTZ黑洞热描述的局限性。我们从物理基础上推导出三个基本的质量尺度，这些尺度与描述这些限制有关。2+1维中的普朗克质量表明了黑洞能够发射霍金辐射的极限。我们证明了对于无自旋BTZ黑洞，反反应是没有意义的。对于静止BTZ黑洞，分析了这种近乎极端的情况，表明它作为热物体的描述可能发生破裂。
Hawking radiation in multi-horizon spacetimes using Hamilton Jacobi method
针对多视界时空的霍金温度由视界间贡献决定的结论，本文用哈密顿-雅可比方法计算三类多视界时空的霍金温度并验证该结论，明确辐射隧穿的两项贡献结合可得到对应有效表面引力的霍金温度。
BTZ black holes and the near-horizon geometry of higher-dimensional black holes
我们研究了BTZ黑洞和高维黑洞的近视界几何之间的联系。在较弱的条件下，我们证明了：（i）如果黑洞具有非极值Reissner-Nordstrom黑洞类型的全局结构，那么它的近视界几何是$AdS_2$乘一个球;（ii）如果这样的黑洞是由一个提升黑弦通过降维得到的，那么后者的近视界几何包含一个BTZ黑洞.由于这些事实，在适当的条件下，标量场的Bekenstein-Hawking熵和吸收截面的计算实质上简化为BTZ几何中相应的计算.即使几何在极值极限上不是超对称的，这也成立。几个例子进行了讨论。我们还讨论了一些推广的几何没有$AdS$附近的地平线。
Noncommutative geometry is an established potential candidate for including quantum phenomena in gravitation. We outline the formalism of Hopf algebras and its connection to the algebra of infinitesimal diffeomorphisms. Using a Drinfeld twist we deform spacetime symmetries, algebra of vector fields and differential forms leading to a formulation of noncommutative Einstein equations. We study a concrete example of charged BTZ spacetime and deformations steaming from the so called angular twist. The entropy of the noncommutative charged BTZ black hole is obtained using the brick-wall method. We …
Quantum gravitational corrections to the stress-energy tensor around the rotating BTZ black hole
从坍缩的黑洞中出现的模式会发生红移，以至于在未来的零无穷远处的霍金辐射包含了在过去的零无穷远处能量超过普朗克尺度的模式。这表明普朗克尺度下的物理学可能会改变霍金辐射的光谱和量子场的相关应力-能量张量。最近的研究表明，弦涨落沿紧额外维的T-对偶性导致了量子场论点粒子标准传播子的修正。在低能量下（与弦尺度相比），我们发现修正的传播子的行为就好像时空具有一个最小长度，比如说$\lp$，我们假设它是普朗克长度的量级。我们利用对偶方法计算了旋转Banados-Teitelboim-Zanelli黑洞周围的修正传播子，并证明了在重合极限下传播子是有限的.我们计算的应力-能量张量与修改后的格林函数和图形说明，量子引力修正原来是可以忽略不计的小。最后，我们简要地评论一下我们所取得的成果。
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