White hole cosmology and Hawking radiation from quantum cosmological perturbations

Abstract

The spacetime inside the white hole is like an anisotropic cosmological background with the past singularity playing the role of a big bang singularity. The scale factor along the extended spatial direction is contracting while the scale factor along the two-sphere is expanding. We consider an eternal Schwarzschild manifold and study quantum cosmological perturbations generated near the white hole singularity which propagate towards the past event horizon and to the exterior of the black hole. It is shown that an observer deep inside the white hole and an observer far outside the black hole both share the same vacuum. We calculate the Hawking radiation associated to these quantum white hole perturbations as measured by an observer in the exterior of the black hole. Furthermore, we also consider the Hawking radiation for the general case where the initial cosmological perturbations deep inside the white hole are in a ``nonvacuum'' state yielding to a deviation from Planck distribution. This analysis suggests that if the black hole is not entirely black (due to Hawking radiation) then the white hole is not entirely white either.