Black Hole Mechanics for Massive Gravitons

Understand

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.