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.
Highlights
Introduction and motivationThe true nature of black holes is already problematic in the classical description given by general relativity and notoriously more so once one tries to incorporate the unavoidable quantum physics
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
Summary
The true nature of black holes is already problematic in the classical description given by general relativity and notoriously more so once one tries to incorporate the unavoidable quantum physics. This suggests that the source of highly compact configurations, such as black holes, must be matter in a quantum state with no purely classical analogue (like Bose–Einstein condensates [15,16,17,18,19,20,21] or degenerate neutron stars) This result is again consistent with the fact that classical general relativistic configurations are expected to become physically relevant only for astrophysical objects with small compactness RH/R 1.
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