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arXiv 1506.01282gr-qchep-th
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爱因斯坦-麦克斯韦理论中熵原理的证明

Proof of entropy principle in Einstein-Maxwell theory

Xiongjun Fang, Sijie Gao

摘要:

在Einstein-Maxwell理论中考虑了一个静态的自引力荷电理想流体系统。假设满足麦克斯韦方程和爱因斯坦约束方程,流体的温度服从托尔曼定律。然后,我们证明了流体的总熵达到一个极值意味着爱因斯坦方程的其他组件的任何变化的度量和电位与固定的边界值。相反,如果爱因斯坦方程和麦克斯韦方程成立,则总熵达到极值。我们的工作表明,当考虑电场时,最大熵原理与爱因斯坦方程是一致的。

英文摘要:

We consider a static self-gravitating charged perfect fluid system in the Einstein-Maxwell theory. Assume Maxwell's equation and the Einstein constraint equation are satisfied, and the temperature of the fluid obeys Tolman's law. Then we prove that the total entropy of the fluid achieves an extremum implies other components of Einstein's equation for any variations of metric and electrical potential with fixed boundary values. Conversely, if Einstein's equation and Maxwell's equations hold, the total entropy achieves an extremum. Our work suggests that the maximum entropy principle is consistent with Einstein's equation when electric field is taken into account.

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