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.
Highlights
A sensible argument to tackle down this premise is to assume that our way of modeling gravity should be extensively modified, as we get closer and closer to regions of extreme curvature
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 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
Summary
A sensible argument to tackle down this premise is to assume that our way of modeling gravity should be extensively modified, as we get closer and closer to regions of extreme curvature. As stressed in [5], the Bardeen black hole is an example of a more general class of solutions of the gravitational field equations in which the regular interior is obtained by assuming a vacuum-like equation of state for the matter content below a certain length scale, in strict analogy with the previous discussion This approach, when applied to static spherically symmetric cases, leads to regular black hole solutions with a de Sitter-like core and makes it reasonable to assume that a proper UV-complete theory of gravity should lead to some physically fundamental constraints on the values of the curvature invariants [6]. We conclude the paper with remarks and hints for future research
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