标题： 黑洞视界可以隐藏正的比热容 显示英文标题

标题： Black hole horizons can hide positive heat capacity

摘要： 将体积视为独立的热力学变量，我们指出黑洞视界可以隐藏正的比热容和比热。 这些视界在机械上是临界的，但在热力学上是稳定的。 在没有规范体积定义的情况下，我们考虑了各种与视界半径不同比例的建议。 假设熵的欧拉齐次性，除了霍金温度外，压力和相应的做功项使得在任何比视界面积更大的体积概念下，视界处的状态方程在热力学上是稳定的。 当也考虑视界处类似斯特藩-玻尔兹曼辐射的状态方程时，只有一个可能的解出现：克里斯托多卢-罗韦利体积，其比例为$V\sim R^5$，具有熵$S = \frac{8}{3}S_{BH}$。 显示英文摘要

摘要： Regarding the volume as independent thermodynamic variable we point out that black hole horizons can hide positive heat capacity and specific heat. Such horizons are mechanically marginal, but thermally stable. In the absence of a canonical volume definition, we consider various suggestions scaling differently with the horizon radius. Assuming Euler-homogeneity of the entropy, besides the Hawking temperature, a pressure and a corresponding work term render the equation of state at the horizon thermally stable for any meaningful volume concept that scales larger than the horizon area. When considering also a Stefan--Boltzmann radiation like equation of state at the horizon, only one possible solution emerges: the Christodoulou--Rovelli volume, scaling as $V\sim R^5$, with an entropy $S = \frac{8}{3}S_{BH}$.