On the gravitational energy of the Hawking wormhole

TL;DR

This paper calculates the gravitational energy of the Hawking wormhole in a conformally flat spacetime using the Hawking-Hunter formalism, revealing a finite Hamiltonian proportional to Rindler acceleration and relating temperature to the Davies-Unruh effect.

Contribution

It applies the Hawking-Hunter formalism to a non-asymptotically flat spacetime representing the Hawking wormhole, deriving the gravitational Hamiltonian and temperature characteristics.

Findings

Gravitational Hamiltonian is proportional to Rindler acceleration g.

Hamiltonian is finite at the event horizon ksi = b.

System temperature relates to Davies-Unruh temperature up to a constant.

Abstract

The surface energy for a conformally flat spacetime which represents the Hawking wormhole in spherical (static) Rindler coordinates is computed using the Hawking - Hunter formalism for non asymptotically - flat spacetimes. The physical gravitational Hamiltonian is proportional to the Rindler acceleration g of the hyperbolic observer and is finite on the event horizon ksi = b (b-the Planck length, ksi - the Minkowski interval). The corresponding temperature of the system of particles associated to the massless scalar field Psi, coupled conformally to Einstein's equations, is given by the Davies - Unruh temperature up to a constant factor of order unity.