具有恰当守恒荷的黑洞精化热力学
Refined Thermodynamics of Black Holes with Proper Conserved Charges
AI总结：
本文利用背景Killing荷方法重新定义黑洞质量与角动量，研究该方法如何改变Kerr-AdS黑洞及Einstein-Gauss-Bonnet黑洞的热力学，并给出无宇宙学常数时的有效体积。
摘要：
经典几何引力理论的场方程，辅以某些半经典考虑，强烈表明代表稳态黑洞的引力场可以简单地用少数热力学坐标及其共轭量来描述，这些量遵循热力学四定律、Smarr公式以及反向等周不等式，后者在给定空间有效体积时限制了最大熵。黑洞热力学是窥探黑洞量子本性的一个有前景的窗口；因此，理解这些定律的所有细节十分重要。这些热力学坐标的识别及其含义取决于所考虑的引力理论。例如，有量纲耦合常数（如宇宙学常数）的存在会改变理论、其解以及热力学定律的标度性质。在此我们展示，利用背景Killing荷方法（该方法适用于任何具有最大对称真空的引力理论的黑洞解）来定义质量和角动量，而不是使用Komar质量和角动量，诸如宇宙学爱因斯坦理论中D维Kerr-AdS黑洞以及Einstein-Gauss-Bonnet理论中球对称黑洞的热力学如何发生变化。我们甚至在不存在宇宙学常数的情况下也给出了黑洞的有效体积。
英文摘要：
Field equations of a classical, geometric, theory of gravity, augmented with some semiclassical considerations strongly suggest that the gravitational field representing a stationary black hole can be simply described with a few thermodynamical coordinates and their conjugates that obey the four laws of thermodynamics plus the Smarr formula and the reverse isoperimetric inequality that bounds the maximum entropy for a given effective volume of space. The thermodynamics of black holes is a promising window to the quantum nature of black holes; hence, it is important to understand all the details of these laws. The identification and the meaning of these thermodynamic coordinates depend on the gravity theory under consideration. For example, the existence of dimensionful coupling constants, such as the cosmological constant, changes the scaling properties of the theory, its solutions, and the laws of thermodynamics. Here we show, using the background Killing charge method, which applies to the black hole solutions of any gravity theory that has a maximally symmetric vacuum, to define the mass and angular momentum, instead of using the Komar mass and the angular momentum, how the thermodynamics of black holes such as the $D$ dimensional Kerr-AdS black holes in cosmological Einstein's theory and the spherically symmetric black holes in the Einstein-Gauss-Bonnet theory changes. We give the effective volume of black holes even without a cosmological constant.
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