Black Hole Mechanics for Massive Gravitons

TL;DR

This paper demonstrates that black holes in massive gravity can have time-independent horizons under certain conditions, derives their thermodynamic laws non-perturbatively, and applies findings to dRGT massive gravity.

Contribution

It establishes a non-perturbative, model-independent framework for black hole horizons in massive gravity and derives their thermodynamic laws.

Findings

Horizon location is time-independent if null with respect to a fiducial Minkowski metric.

A second law of black hole mechanics is derived for these solutions.

Consistent solutions in dRGT massive gravity are found with specific horizon properties.

Abstract

It has been argued that black hole solutions become unavoidably time-dependent when the graviton has a mass. In this work we show that, if the apparent horizon of the black hole is a null surface with respect to a fiducial Minkowski reference metric, then the location of the horizon is necessarily time-independent, despite the dynamical metric possessing no time-like Killing vector. This result is non-perturbative and model-independent. We derive a second law of black hole mechanics for these black holes and determine their surface gravity. An additional assumption establishes a zeroth and a first law of black hole mechanics. We apply these results to the specific model of dRGT ghost-free massive gravity and show that consistent solutions exist which obey the required assumptions. We determine the time-dependent scalar curvature at the horizon of these black holes.