【摘 要】
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Thermodynamics plays an important role in gravitational theories.It is a principle that is independent of gravitational dynamics,and there is still no rigorous proof to show that it is consistent with the dynamical principle.We consider a self-gravitating
【机 构】
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Department of Physics,Key Laboratory of Low Dimensional Quantum Structures and Quantum Control of Mi
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Thermodynamics plays an important role in gravitational theories.It is a principle that is independent of gravitational dynamics,and there is still no rigorous proof to show that it is consistent with the dynamical principle.We consider a self-gravitating perfect fluid system with the general diffeomorphism-covariant purely gravitational theory.Based on the Noether charge method proposed by Iyer and Wald,considering static off/on-shell variational configurations,which satisfy the gravitational constraint equation,we rigorously prove that the extrema of the total entropy of a perfect fluid inside a compact region for a fixed total particle number demands that the static configura-tion is an on-shell solution after we introduce some appropriate boundary conditions,i.e.,it also satisfies the spatial gravitational equations.This means that the entropy principle of the fluid stores the same information as the gravita-tional equation in a static configuration.Our proof is universal and holds for any diffeomorphism-covariant purely gravitational theories,such as Einstein gravity,f(R)gravity,Lovelock gravity,f(Gauss-Bonnet)gravity and Ein-stein-Weyl gravity.Our result indicates the consistency between ordinary thermodynamics and gravitational dynam-ics.
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