General proof of the principle for self-gravitating fluid in static spacetimes
General proof of the principle for self-gravitating fluid in static spacetimes
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静态时空中自引力流体原理的一般证明
DOI：
10.1103/physrevd.90.044013
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
高思杰
中科院分区：
文献类型：
--
作者：
高思杰
我们证明了对于静态时空中的任何完美流体，如果满足爱因斯坦约束方程，并且流体的温度服从托尔曼定律，那么爱因斯坦方程的其他分量可以通过假设流体的总熵在固定的总粒子数和具有一定边界条件的所有度规变化下达到极值来隐含。相反，我们可以证明，流体的总熵的极值是由爱因斯坦的方程隐含的。与以往的研究相比，我们不再要求时空具有球对称性。我们的结果表明热力学和广义相对论之间存在着普遍而坚实的联系。
We show that for any perfect fluid in a static spacetime, if the Einstein constraint equation is satisfied and the temperature of the fluid obeys Tolman's law, then the other components of Einstein's equation are implied by the assumption that the total entropy of the fluid achieves an extremum for fixed total particle number and for all variations of metric with certain boundary conditions. Conversely, one can show that the extrema of the total entropy of the fluid are implied by Einstein's equation. Compared to previous works on this issue, we do not require spherical symmetry for the spacetime. Our results suggest a general and solid connection between thermodynamics and general relativity.