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

Abstract

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.

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

References in corpus (7)

• Horizon Entropy
• Relativistic conservation laws and integral constraints for large cosmological perturbations
• de Sitter Black Holes with Either of the Two Horizons as a Boundary
• Thermodynamics of $(d+1)$-dimensional NUT-charged AdS Spacetimes
• Expanding the Area of Gravitational Entropy
• Conserved Quantities from the Equations of Motion (with applications to natural and gauge natural theories of gravitation)
• Covariant Charges in Chern-Simons AdS_3 Gravity

Cited by in corpus (2)

• Action growth for black holes in modified gravity
• The relative energy of homogeneous and isotropic universes from variational principles