Black hole solutions in massive gravity

TL;DR

This paper explores static vacuum spherically symmetric solutions in massive gravity, revealing modified black holes with unique properties such as scalar charge dependence, potential anti-gravity effects, and mimicking dark matter at intermediate scales.

Contribution

It provides the first comprehensive analytical and numerical analysis of black hole solutions in massive gravity, including the role of scalar charge and stability considerations.

Findings

Standard Schwarzschild solutions recovered at zero scalar charge.

Existence of modified black holes with or without horizons depending on parameters.

Modified solutions can exhibit anti-gravity and mimic dark matter effects.

Abstract

The static vacuum spherically symmetric solutions in massive gravity are obtained both analytically and numerically. The solutions depend on two parameters (integration constants): the mass M (or, equivalently, the Schwarzschild radius), and an additional parameter, the "scalar charge" S. At zero value of S and positive mass the standard Schwarzschild black hole solutions are recovered. Depending on the parameters of the model and the signs of M and S, the solutions may or may not have horizon. Those with the horizon describe modified black holes provided they are stable against small perturbations. In the analytically solvable example, the modified black hole solutions may have both attractive and repulsive (anti-gravitating) behavior at large distances. At intermediate distances the gravitational potential of a modified black hole may mimics the presence of dark matter. Modified black hole solutions are also found numerically in more realistic massive gravity models which are attractors of the cosmological evolution.