Stars and (Furry) Black Holes in Lorentz Breaking Massive Gravity

TL;DR

This paper explores exact black hole solutions in Lorentz-breaking massive gravity, revealing unique features like non-analytic hair and effective mass renormalization, with implications for dark energy and graviton mass limits.

Contribution

It provides explicit spherically symmetric black hole solutions in Lorentz-breaking massive gravity and analyzes their novel physical properties and observational implications.

Findings

Black hole solutions with non-analytic hair in massive gravity.

Effective renormalization of gravitational mass linked to body size.

Upper limit on graviton mass from stability of bound states.

Abstract

We study the exact spherically symmetric solutions in a class of Lorentz-breaking massive gravity theories, using the effective-theory approach where the graviton mass is generated by the interaction with a suitable set of Stuckelberg fields. We find explicitly the exact black hole solutions which generalizes the familiar Schwarzschild one, which shows a non-analytic hair in the form of a power-like term r^\gamma. For realistic self-gravitating bodies, we find interesting features, linked to the effective violation of the Gauss law: i) the total gravitational mass appearing in the standard 1/r term gets a multiplicative renormalization proportional to the area of the body itself; ii) the magnitude of the power-like hairy correction is also linked to size of the body. The novel features can be ascribed to presence of the goldstones fluid turned on by matter inside the body; its equation of state approaching that of dark energy near the center. The goldstones fluid also changes the matter equilibrium pressure, leading to an upper limit for the graviton mass, m <~ 10^-28 - 10^29 eV, derived from the largest stable gravitational bound states in the Universe.