Dynamics of gravitational field within a wave front and thermodynamics of black holes

Abstract

Hamiltonian dynamics of gravitational field contained in a spacetime region with boundary $S$ being a null-like hypersurface (a wave front) is discussed. Complete Hamiltonian formula for the dynamics (with no surface integrals neglected) is derived. A quasi-local proof of the first law of black holes thermodynamics is obtained as a consequence, in case when $S$ is a non-expanding horizon. The zeroth law and Penrose inequalities are discussed from this point of view.

14 pages, 2 figures

Cited by in corpus (10)

• Null Conservation Laws for Gravity
• Mechanics of multidimensional isolated horizons
• Universality of affine formulation in General Relativity theory
• Symmetric non-expanding horizons
• The Hamiltonian mass of asymptotically Schwarzschild-de Sitter space-times
• Quasi--local angular momentum of non--symmetric isolated and dynamical horizons from the conformal decomposition of the metric
• Hamiltonian dynamics in the space of asymptotically Kerr-de Sitter spacetimes
• Local approach to thermodynamics of black holes
• Gluing variations
• Dynamics of a self gravitating light-like matter shell with spherical symmetry