Eternal Black Holes and Quasilocal Energy

TL;DR

This paper derives the gravitational action, Hamiltonian, and quasilocal energy for an eternal black hole with a bifurcation surface, extending previous analyses and suggesting a generalized thermodynamic interpretation based on thermofield dynamics.

Contribution

It explicitly constructs the Hamiltonian and quasilocal energy for eternal black holes with boundaries, extending prior work to more complex spacetime regions.

Findings

Hamiltonian expressed as difference of boundary Hamiltonians

Explicit construction of quasilocal energy for black hole regions

Implication for generalized black hole thermodynamics

Abstract

We present the gravitational action and Hamiltonian for a spatially bounded region of an eternal black hole. The Hamiltonian is of the general form $H=H_{+} - H_{-}$, where $H_{+}$ and $H_{-}$ are respectively the Hamiltonians for the regions $M_+$ and $M_-$ located in the left and right wedges of the spacetime. We construct explicitly the quasilocal energy for the system and discuss its dependence on the time direction induced at the boundaries of the manifold. This paper extends the analysis of Ref.~[1] to spacetimes possesing a bifurcation surface and two timelike boundaries. The construction suggests that an interpretation of black hole thermodynamics based on thermofield dynamics ideas can be generalized beyond perturbations to the gravitational field itself of a bounded spacetime region (based on the talk presented by E.A. Martinez at the Lake Louise Winter School on Particle Physics and Cosmology, February 20-26, 1994.)