Sourcing a Varying-Mass Black Hole in a Cosmological Background

Abstract

Systems in which the local gravitational attraction is coupled to the expansion of the Universe have been studied since the early stages of General Relativity. The McVittie metric is an example of such systems, being an exact solution of the Einstein equations representing a black hole in a cosmological background. Here, by using imperfect fluids, we construct a generalization of the McVittie solution in which the mass function of the black hole increases with time, effectively describing an accreting compact object in an expanding Universe. A novel mechanism involving temperature gradients is the key ingredient that leads to this result while still avoiding phantom fields and fine-tuning.