The horizon of the lightest black hole

Abstract

We study the properties of the poles of the resummed graviton propagator obtained by resumming bubble matter diagrams which correct the classical graviton propagator. These poles have been previously interpreted as black holes precursors. Here, we show using the horizon wavefunction formalism that these poles indeed have properties which make them compatible with being black hole precursors. In particular, when modeled with a Breit-Wigner distribution, they have a well-defined gravitational radius. The probability that the resonance is inside its own gravitational radius, and thus that it is a black hole, is about one half. Our results confirm the interpretation of these poles as black hole precursors.

Global and local horizon quantum mechanics

“…We have thus recovered the HWF [11] 15) where the values R Hα form a discrete (continuous) spectrum if E α is discrete (continuous) in the quantum number α. If the spectral decomposition (2.4) is continuous, so will be the HWF, and we can write 16) with N −2…”

“…The HQM can therefore be viewed as complementary to approaches which consider the horizon and black holes as purely gravitational (or metric) objects, in that the gravitational degrees of freedom are taken "on-shell" with respect to a suitable constraint with the matter state. The HQM can then be naturally applied to systems which do not turn out to be black holes, that is, to matter systems with a negligible probability of being black holes, or to objects "on the verge" of being black holes [15].…”

“…Clearly, the HQM becomes particularly relevant for sources of the Planck size [15,18], for which quantum effects may not be neglected. The Heisenberg principle of quantum mechanics introduces an uncertainty in the particle's spatial localisation of the order of the Compton-de Broglie length, λ M ≃ ℓ p m p /M, and R H only makes sense if…”

Quantum production of black holes at colliders

“…The HQM for static sources [19][20][21][22][23][24] was extended to higher dimensions in Refs. [18,25], which can be naturally applied to BHs in the ADD scenario.…”

“…[18] from the Horizon Quantum Mechanics (HQM) of localised sources [19][20][21][22][23][24][25]. In fact, this approach was specifically devised to yield the probability that a particle is a BH, and is therefore perfectly suited to address this issue.…”