Obstruction of black hole singularity by quantum field theory effects

Abstract

Abstract:We consider the back reaction of the energy due to quantum fluctuation of the background fields considering the trace anomaly for Schwarzschild black hole. It is shown that it will result in modification of the horizon and also formation of an inner horizon. We show that the process of collapse of a thin shell stops before formation of the singularity at a radius slightly smaller than the inner horizon at the order of (c A M Mp ) 1/3 l p . After the collapse stops the reverse process takes place. Thus we demonstrate that without turning on quantum gravity and just through the effects the coupling of field to gravity as trace anomaly of quantum fluctuations the formation of the singularity through collapse is obstructed. An important consequence of our work is existence of an extremal solution with zero temperature and a mass which is lower bound for the Schwazschild solution. This solution is also the asymptotic final stable state after Hawking radiation.

Quantum vacuum effects on the final fate of a collapsing ball of dust

“…, the results will be similar to the results in [18] for conformally coupled fields. The solutions of Einstein's equations are easily obtained as…”

“…In this paper we use a semi-classical approach to the final fate of a collapsing homogeneous ball of dust by taking into account the vacuum expectation value of the stress-energy tensor of quantum scalar fields that are arbitrarily coupled to the background geometry of the collapsing object. In [18], it was shown that for the special case of conformally invariant fields of arbitrary spin, the quantum vacuum effects are capable of preventing a collapsing thin shell of matter from reaching the singularity. A bounce radius at which the collapse of the shell stops and the direction of the movement reverses was predicted.…”

A Model of Black Hole Evaporation and 4D Weyl Anomaly

“…20 We can see explicitly this by constructing the Tolman-Oppenheimer-Volkoff equation with T r r = T θ θ and using − T t t , T r r T θ θ . 21 See also [33]. 22 The entropy can also be understood by the matter in the interior.…”

“…Then, we introduce V as a label of an ingoing null line following (3): once an initial position for r(U) in (3) is given, the solution is determined uniquely, which we denote byr(U, V). This plays roles of r(U, V) in (33). Indeed, we have:…”

“…First we determine T µν in the interior metric (83), which can be expressed by (33) with (81). We assume (80) and express the relation (73) as:…”