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Abstract
摘要 |
We show that for any perfect fluid in a static spacetime, if Einstein’s equation is satisfied and the temperature of the fluid obeys Tolman’s law, then the total entropy of the fluid must achieve an extremum for all variations of metric with fixed boundary values and fixed total particle numbers. Conversely, if the Einstein constraint equation holds and the total entropy is an extremum, the other components of Einstein’s equation are implied. Compared to previous works on this issue, we do not require spherical symmetry for the fluid. Our results suggest a general and solid connection between thermodynamics and general relativity. |
