[论文解读] Classical Black Holes Are Hot

Erik Curiel|PhilSci-Archive (University of Pittsburgh)|Aug 16, 2014

Cosmology and Gravitation Theories参考文献 44被引用 3

一句话总结

本文主张，在广义相对论中，经典黑洞可作为热力学系统处理，而无需引入量子力学，通过证明表面引力和视界面积在经典卡诺类循环中分别扮演温度和熵的角色。其关键贡献在于证明黑洞力学与热力学之间的类比在经典广义相对论框架内具有物理意义且自洽。

ABSTRACT

In the early 1970s it is was realized that there is a striking formal analogy between the Laws of black-hole mechanics and the Laws of classical thermodynamics. Before the discovery of Hawking radiation, however, it was generally thought that the analogy was only formal, and did not reflect a deep connection between gravitational and thermodynamical phenomena. It is still commonly held that the surface gravity of a stationary black hole can be construed as a true physical temperature and its area as a true entropy only when quantum effects are taken into account; in the context of classical general relativity alone, one cannot cogently construe them so. Does the use of quantum field theory in curved spacetime offer the only hope for taking the analogy seriously? I think the answer is `no'. To attempt to justify that answer, I shall begin by arguing that the standard argument to the contrary is not physically well founded, and in any event begs the question. Looking at the various ways that the ideas of "temperature" and "entropy" enter classical thermodynamics then will suggest arguments that, I claim, show the analogy between classical black-hole mechanics and classical thermodynamics should be taken more seriously, without the need to rely on or invoke quantum mechanics. In particular, I construct an analogue of a Carnot cycle in which a black hole "couples" with an ordinary thermodynamical system in such a way that its surface gravity plays the role of temperature and its area that of entropy. Thus, the connection between classical general relativity and classical thermodynamics on their own is already deep and physically significant, independent of quantum mechanics.

研究动机与目标

• 挑战一种普遍观点，即黑洞的热力学类比仅在包含霍金辐射等量子效应时才成立。
• 论证仅凭经典广义相对论已足够为将黑洞视为热力学系统提供基础。
• 通过在经典框架下重新诠释热力学概念，解决一个理想吸收体（经典黑洞）为何可具有非零温度的明显悖论。
• 表明黑洞力学定律与经典热力学定律并非仅仅是形式类比，而是反映了深刻的物理联系。
• 通过与经典热力学类比，解决引力系统中能量非局域性与热量传递的 foundational 问题。

提出的方法

• 构建一个涉及史瓦西黑洞与经典热力学系统的经典卡诺循环类比。
• 将黑洞的表面引力作为温度的代理，其视界面积作为熵的代理。
• 将热力学循环的形式结构应用于黑洞，表明能量交换与功的提取在概念上是自洽的。
• 依赖于静态轴对称时空中的准局域质量-能量定义，以避免引力能量非局域性带来的问题。
• 指出引力能量的非局域性与经典热力学中热量的非局域性具有相似之处。
• 将熵重新解释为可提取功的度量，而非统计量，从而解释视界形成时熵的不连续跃迁。

实验结果

研究问题

• RQ1 经典黑洞是否可在不引入弯曲时空中量子场论的前提下，被视为热力学系统？
• RQ2 黑洞力学与热力学之间的类比是否仅为形式上的，还是在经典广义相对论中反映了更深层次的物理联系？
• RQ3 为何一个作为理想吸收体的黑洞（其温度为零）仍可通过表面引力被赋予非零温度？
• RQ4 若不基于统计力学，黑洞熵的物理意义是什么？
• RQ5 如何在热力学一致的前提下，实现全局量（如ADM质量）与局域应力-能量之间的能量交换？

主要发现

• 经典黑洞无法具有温度或熵的标准论据在物理上站不住脚，且存在循环论证的嫌疑。
• 可构建一个经典卡诺-杰罗赫循环，其中黑洞的表面引力充当温度，面积充当熵，从而在无量子输入的情况下展示热力学行为。
• 引力能量的非局域性并不妨碍热力学推理，因为经典热力学中的热量同样非局域且无局域密度。
• 黑洞中的熵可理解为自由能与可提取功的度量，从而解释视界形成时熵的不连续跃迁。
• 黑洞力学定律是微分几何的定理，其推导无需依赖爱因斯坦场方程，而热力学定律则是经验性的。
• 黑洞力学与热力学之间类比的深层物理意义可独立于量子力学确立，表明黑洞热力学具有经典基础。