标题： 热力学和双曲空间上的引力不稳定性 显示英文标题

标题： Thermodynamic and gravitational instability on hyperbolic spaces

摘要： 我们研究了具有高斯-博内项的反德西特黑洞的各种视界拓扑（k=0,\pm 1）和不同维度的性质，特别关注不太为人所知的k=-1解。 我们发现，零温度（和零能量密度）的极端状态是具有双曲事件视界的AdS黑洞的能量局部最小值。 当背景由极端解定义且极端熵为非负时，双曲AdS黑洞可能在热力学上是稳定的。 我们还研究了D>4维的AdS时空对线性扰动的引力稳定性，并发现极端状态仍然是能量的局部最小值。 对于球对称的AdS黑洞解，引力势是正的且有界的，无论是否有高斯-博内型修正，而当k=-1时，一个小的高斯-博内耦合，即\alpha <<{l}^2（其中l是AdS空间的曲率半径），被发现有助于保持势能从下方有界，这是极端背景稳定性的要求。 显示英文摘要

摘要： We study the properties of anti--de Sitter black holes with a Gauss-Bonnet term for various horizon topologies (k=0, \pm 1) and for various dimensions, with emphasis on the less well understood k=-1 solution. We find that the zero temperature (and zero energy density) extremal states are the local minima of the energy for AdS black holes with hyperbolic event horizons. The hyperbolic AdS black hole may be stable thermodynamically if the background is defined by an extremal solution and the extremal entropy is non-negative. We also investigate the gravitational stability of AdS spacetimes of dimensions D>4 against linear perturbations and find that the extremal states are still the local minima of the energy. For a spherically symmetric AdS black hole solution, the gravitational potential is positive and bounded, with or without the Gauss-Bonnet type corrections, while, when k=-1, a small Gauss-Bonnet coupling, namely, \alpha << {l}^2 (where l is the curvature radius of AdS space), is found useful to keep the potential bounded from below, as required for stability of the extremal background.