``Physical process version'' of the first law and the generalized second law for charged and rotating black holes
``Physical process version'' of the first law and the generalized second law for charged and rotating black holes
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DOI：
10.1103/physrevd.64.084020
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发表时间：
2001-06
影响因子：
5
通讯作者：
Sijie Gao;R. Wald
中科院分区：
文献类型：
--
作者：
Sijie Gao;R. Wald
我们调查的“物理过程”版本的第一定律和广义第二定律的黑洞热力学带电和旋转黑洞。我们开始推导出了一阶变分的Arnowitt-Deser-Misner质量和角动量的一般公式，线性扰动离开一个固定的，电真空背景的扰动非电磁应力能量$\ensuremath{\delta}{T}_{ab}}$和扰动电荷电流密度$\ensuremath{\delta}{j}^{a}。利用这些公式，我们证明了带电静止黑洞第一定律的“物理过程版本”。然后，我们研究了广义热力学第二定律（GSL）带电，静止黑洞的过程中，一个盒子含有带电物质降低到黑洞，然后释放（在这一点上，盒子和它的内容落入黑洞和/或热化与“热大气”周围的黑洞）。假设热大气承认一个本地的，热力学描述相对于观察者以下的地平线Killing场的轨道，并假设组合的黑/hole\char21{}热大气系统是在一个状态的最大熵在固定的质量，角动量，和电荷，我们表明，总广义熵不能减少在降低过程中或在"释放过程“。因此，GSL在这样的过程中总是成立的。在我们的任何论证中，都没有假定物质的熵界限成立。
We investigate both the ``physical process'' version of the first law and the generalized second law of black hole thermodynamics for charged and rotating black holes. We begin by deriving general formulas for the first order variation in the Arnowitt-Deser-Misner mass and angular momentum for linear perturbations off a stationary, electrovac background in terms of the perturbed nonelectromagnetic stress-energy $\ensuremath{\delta}{T}_{\mathrm{ab}}$ and the perturbed charge current density $\ensuremath{\delta}{j}^{a}.$ Using these formulas, we prove the ``physical process version'' of the first law for charged, stationary black holes. We then investigate the generalized second law of thermodynamics (GSL) for charged, stationary black holes for processes in which a box containing charged matter is lowered toward the black hole and then released (at which point the box and its contents fall into the black hole and/or thermalize with the ``thermal atmosphere'' surrounding the black hole). Assuming that the thermal atmosphere admits a local, thermodynamic description with respect to observers following orbits of the horizon Killing field, and assuming that the combined black/hole\char21{}thermal atmosphere system is in a state of maximum entropy at fixed mass, angular momentum, and charge, we show that the total generalized entropy cannot decrease during the lowering process or in the ``release process.'' Consequently, the GSL always holds in such processes. No entropy bounds on matter are assumed to hold in any of our arguments.