Black holes in a dense infinite medium: a toy-model regularizing the Schwarzschild metric

We revisit the dynamics of a black hole accreting energy from a surrounding homogeneous and infinite space. We argue for a simple heuristic modification of the Schwarzschild approximation when the density of the medium is not negligible anymore. The resulting behavior is drastically modified: the mass divergence at finite time is cured and the thermodynamical properties are deeply changed. Some potential consequences for quantum gravity and bouncing models are also pointed out. Those conclusions being mostly obtained from a Newtonian approach, they only aim at guiding toward a more rigorous treatment. Still, interestingly, the behavior is far more convincing that the one usually obtained.