Back-reaction of the Hawking radiation flux on a gravitationally collapsing star II

Abstract

A star collapsing gravitationally into a black hole emits a flux of radiation, known as Hawking radiation. When the initial state of a quantum field on the background of the star, is placed in the Unruh vacuum in the far past, then in the exterior Hawking radiation corresponds to a flux of positive energy radiation travelling outwards from near the surface to future infinity. Based on pair creation, the evaporation of the collapsing star can be equivalently described by the absorption of an ingoing negative energy flux of radiation travelling towards the center of the star. Here, we are interested in the evolution of the star during its collapse. Thus we include the backreaction of the negative energy Hawking flux in the interior geometry of the collapsing star when writing the full 4-dimensional Einstein and hydrodynamic equations. Hawking radiation emitted before the star passes through its Schwarzschild radius slows down and reverses the collapse of the star. The star evaporates without forming an horizon or a singularity. This study provides a more realistic investigation than the one first presented in [1], since the backreaction of Hawking radiation flux on the collapsing star is studied in the case when the initial state of the field is in Unruh's vacuum.