General proof of the entropy principle for self-gravitating fluid in static spacetimes

Abstract

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.

11 pages, no figure. Order of the two theorems exchanged, matches published version

References in corpus (4)

• Friedmann Equations and Thermodynamics of Apparent Horizons
• Dynamic and Thermodynamic Stability of Relativistic, Perfect Fluid Stars
• Maximum Entropy Principle for Self-gravitating Perfect Fluid in Lovelock Gravity
• Gravitational-thermodynamic instabilities of isothermal spheres in dS and AdS

Cited by in corpus (16)

• Statistical mechanics of self-gravitating systems in general relativity: I. The quantum Fermi gas
• Relativistic Gravothermal Instabilities
• Is gravity entropic force?
• Gravitational instability caused by the weight of heat
• Holographic bounds and finite inflation
• Proof of entropy principle in Einstein-Maxwell theory
• Thermodynamical stability for perfect fluid
• Classifying self-gravitating radiations
• General proof of (maximum) entropy principle in Lovelock gravity
• Stationarity of Extremum Entropy Fluid Bodies in General Relativity
• Consistency between dynamical and thermodynamical stabilities for perfect fluid in $f(R)$ theories
• Thermodynamic equilibrium condition and the first law of thermodynamics for charged perfect fluids in electromagnetic and gravitational fields
• Gravitational potential from maximum entropy principle
• Heat capacity of a self-gravitating spherical shell of radiations
• Consistency between dynamical and thermodynamical stabilities for charged self-gravitating perfect fluid
• Universality of entropy principle for a general diffeomorphism-covariant purely gravitational theory