Bootstrapped Newtonian stars and black holes

Abstract

We study equilibrium configurations of a homogenous ball of matter in a bootstrapped description of gravity which includes a gravitational self-interaction term beyond the Newtonian coupling. Both matter density and pressure are accounted for as sources of the gravitational potential for test particles. Unlike the general relativistic case, no Buchdahl limit is found and the pressure can in principle support a star of arbitrarily large compactness. By defining the horizon as the location where the escape velocity of test particles equals the speed of light, like in Newtonian gravity, we find a minimum value of the compactness for which this occurs. The solutions for the gravitational potential here found could effectively describe the interior of macroscopic black holes in the quantum theory, as well as predict consequent deviations from general relativity in the strong field regime of very compact objects.

On the mass of bootstrapped Newtonian sources

“…For this reason, a bootstrapped version of Newtonian gravity that contains non-linear interaction terms was developed in Refs. [3][4][5][6] as a toy model to describe static, spherically symmetric sources in a quantum fashion 1 . Solutions were then found corresponding to homogeneous matter distributions of radius R for which no Buchdahl limit [8] appears, but still require increasingly large pressure to counterbalance the gravitational pull for increasing compactness.…”

“…Since only M can be measured by studying orbits around the compact object, we shall define the compactness in terms of M as G N M/R like in Ref. [6]. One then obtains a unique relation between M 0 and M .…”

“…As a further development of the model, we are here interested in analysing in more detail the effects of the couplings introduced in Ref. [6] on these two masses.…”

“…Following Refs. [3][4][5][6], one can view U N as given by the volume integral of the gravitational current…”

MGD Dirac Stars

“…The MGD was also used in Refs. [29][30][31][32][33][34][35][36][37][38], that include anisotropic solutions of quasi-Einstein equations [1,[39][40][41][42].…”