Action and Hamiltonian for eternal black holes

TL;DR

This paper derives the Hamiltonian, quasilocal energy, and angular momentum for a spacetime region bounded by two timelike surfaces, with applications to eternal black holes and their thermofield dynamics interpretation.

Contribution

It introduces a Hamiltonian framework for eternal black holes with boundaries in different Kruskal wedges, linking classical and quantum descriptions.

Findings

Hamiltonian for eternal black holes expressed as difference of wedge Hamiltonians

Application to thermofield dynamics in black hole quantum effects

Explicit formulas for energy and angular momentum in bounded regions

Abstract

We present the Hamiltonian, quasilocal energy, and angular momentum for a spacetime region spatially bounded by two timelike surfaces. The results are applied to the particular case of a spacetime representing an eternal black hole. It is shown that in the case when the boundaries are located in two different wedges of the Kruskal diagram, the Hamiltonian is of the form $H = H_+ - H_-$, where $H_+$ and $H_-$ are the Hamiltonian functions for the right and left wedges respectively. The application of the obtained results to the thermofield dynamics description of quantum effects in black holes is briefly discussed.