Quasi-local black hole thermodynamics and gravitational pressure

Black hole thermodynamics, in which physical quantities are global, is well established. In realistic astrophysical processes, the quasi-local black hole thermodynamics (thermodynamics in a finite spacetime region) is an essential problem. We develop quasi-local black hole thermodynamics by using the quasi-local energies of gravitation. For the first time, we suggest the concept of gravitational pressure, i.e. the pressure of gravitational field itself in thermodynamics for black holes, and find that it is necessary for quasi-local black hole thermodynamics in asymptotic flat space. We extend quasi-local black hole thermodynamics to the cases of asymptotic de Sitter and anti-de Sitter spaces. This exploration presents new insights into quasi-local energy of gravity, and is much more closely related to realistic astrophysics.