On the gravitational energy of the Hawking wormhole

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.