Abstract
We consider the effects of gravitons in the collapse of baryonic matter that forms a black hole. We first note that the effective number of (soft off-shell) gravitons that account for the (negative) Newtonian potential energy generated by the baryons is conserved and always in agreement with Bekenstein's area law of black holes. Moreover, their (positive) interaction energy reproduces the expected post-Newtonian correction and becomes of the order of the total ADM mass of the system when the size of the collapsing object approaches its gravitational radius. This result supports a scenario in which the gravitational collapse of regular baryonic matter produces a corpuscular black hole without central singularity, in which both gravitons and baryons are marginally bound and form a Bose-Einstein condensate at the critical point. The Hawking emission of baryons and gravitons is then described by the quantum depletion of the condensate and we show the two energy fluxes are comparable, albeit negligibly small on astrophysical scales.
Highlights
One of the main issues in gravity theory is to understand the formation of black holes from the gravitational collapse of compact objects
Our main result is that these gravitons satisfy Bekenstein’s area law [7] and appear to produce the expected postNewtonian correction [8] to the total energy of the system, which becomes a major contribution to the dynamics when the gravitational radius is approached
In rather general terms, that including the effect of soft gravitons in the description of the gravitational collapse of a compact object naturally leads to the expected postNewtonian correction to the energy of the system and to the possible formation of a corpuscular black hole mostly made of gravitons
Summary
One of the main issues in gravity theory is to understand the formation of black holes from the gravitational collapse of compact objects It is a theorem in general relativity [1] that, provided the collapsing (massive) matter satisfies the weak energy condition and a trapping surface appears at some point, all the matter will eventually shrink into a space-time singularity (of infinite density). We will include the effect of (negative energy) gravitons with a wavelength of the order of the size of the collapsing body in the total energy balance These soft gravitons appear in the quantum representation of the Newtonian potential by means of a coherent state coupled to the matter source [3,4], and one might speculate [5] that they could be associated with the recently advocated breaking of the BMS symmetry [6] precisely induced by the presence of localised matter. A black hole should form, mostly made of such soft gravitons (in a sense that will be clarified later on), in qualitative agreement with the corpuscular model of Refs. [9]
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