Boundary Conditions, Energies and Gravitational Heat in General Relativity (a Classical Analysis)

Details Boundary Conditions, Energies and Gravitational Heat in General Relativity (a Classical Analysis) Boundary Conditions, Energies and Gravitational Heat in General Relativity (a Classical Analysis)

2004-02-18

arxiv.org/abs/gr-qc/0402080v2

Class.Quant.Grav. 21 (2004) 3459-3482

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Latex file, 31 pages; one reference and two comments added, misprints corrected

Scientific paper

10.1088/0264-9381/21/14/010

The variation of the energy for a gravitational system is directly defined from the Hamiltonian field equations of General Relativity. When the variation of the energy is written in a covariant form it splits into two (covariant) contributions: one of them is the Komar energy, while the other is the so-called covariant ADM correction term. When specific boundary conditions are analyzed one sees that the Komar energy is related to the gravitational heat while the ADM correction term plays the role of the Helmholtz free energy. These properties allow to establish, inside a classical geometric framework, a formal analogy between gravitation and the laws governing the evolution of a thermodynamic system. The analogy applies to stationary spacetimes admitting multiple causal horizons as well as to AdS Taub-bolt solutions.

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