Horizon quantum fuzziness for non-singular black holes

Abstract

We study the extent of quantum gravitational effects in the internal region of non-singular, Hayward-like solutions of Einstein's field equations according to the formalism known as horizon quantum mechanics. We grant a microscopic description to the horizon by considering a huge number of soft, off-shell gravitons, which superimpose in the same quantum state, as suggested by Dvali and Gomez. In addition to that, the constituents of such a configuration are understood as loosely confined in a binding harmonic potential. A simple analysis shows that the resolution of a central singularity through quantum physics does not tarnish the classical description, which is bestowed upon this extended self-gravitating system by General Relativity. Finally, we estimate the appearance of an internal horizon as being negligible, because of the suppression of the related probability caused by the large number of virtual gravitons.

On the corpuscular theory of gravity

“…(3) H , that allows us to make the identications If we then consider a very small regular core, namely 83) since the total angular momentum of the Hayward space vanishes and we are therefore allowed to limit ourselves to the case l = l 0 = 0, for sake of simplicity. Thus, assuming the Hayward black hole to be the result of (sourced by) a coherent state of these toy gravitons [81], we have that the quantum state of the source, within the framework of the HQM, can therefore be approximated by 84) with r | φ 0 = φ 0 (r). Let us also remark that (4.84) is an eigenstate of the total Hamiltonian H, i.e.…”

“…We can now compute the probability P BH ( ; N ) for this N -particle state to be a black hole. First, following Denition 6, it is easy to see that Besides, we can approximate the total probability density, for the outer horizon, by (see [81])…”

Horizon quantum mechanics for spheroidal sources

“…From the results of the previous section, we expect the HQM for spherically symmetric sources carries on to the spheroidal case straightforwardly. For this reason, we shall not report the details here, but just refer to the existing HQM literature [6][7][8][9][10][11][12][13][14][15]. Nonetheless, we further need an observable to determine the deformation classically parametrised by a.…”

“…Unlike most other attempts, in which the gravitational degrees of freedom are quantised independently, this approach lifts the relation between the state of the source and the state of the gravitational radius to a (local or global) quantum constraint [7,8]. The HQM has already been applied to several cases which can be reduced to isotropic sources [9][10][11][12][13][14][15]. However, its extension to non-spherical systems requires one to identify a mass function from which the location of trapping surfaces can be uniquely determined and which depends only on the state of the matter source, like the Misner-Sharp mass for isotropic sources.…”

Horizon quantum mechanics of collapsing shells

“…We interpret the normalised wave-function ψ H simply as yielding the probability that r = R H is the gravitational radius associated with the particle in the given quantum state ψ S . The localisation of the horizon will consequently be governed by the uncertainty relation, like the position of the particle itself [9][10][11][12][13][14][15][16][17].…”