Quantum radiation from an evaporating non-singular black hole

Abstract

In this paper we study quantum radiation from an evaporating spherically symmetric non-singular black hole. We used a modified Hayward metric for a description of a non-singular black hole. We assume that the mass parameter of this metric depends on the advanced time, and choose this dependence so that it properly reproduces both black hole formation and its subsequent evaporation. We consider a quantum massless scalar field propagating in this geometry and use 2D approximation for the calculation of the quantum average of the stress-energy tensor. For the calculation of this quantity it is sufficient to find a map between the Killing times $u_+$ and $u_-$ at the future and past null infinities, established by the propagation of the radial null rays. In this formalism the quantum energy flux at the future null infinity can be expressed in terms of the function $u_+(u_-)$ and its derivatives. We developed a special formalism, which allows one to reduce the problem of the calculation of the quantum energy flux and other observables to a solution of a simple set of ordinary differential equations. We used this approach to study quantum effects in two cases: i) with the trivial, $\alpha=1$ and ii) the non-trivial, $\alpha\ne1$, redshift function. In both cases there exists an outburst of the quantum energy radiation from the inner domain of the black hole, close to the inner part of its apparent horizon. For $\alpha=1$ this outburst is exponentially large. It is a direct consequence of the so-called mass inflation effect. We showed, that this severe problem can be solved by a proper choice of the redshift function. However, even in this case the emitted energy can be much larger than the initial mass of the evaporating black hole. This means that for a construction of a self-consistent model of a non-singular evaporating black hole the back-reaction effects are highly important.