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.
Highlights
It remains an open question: what would happen to a black hole if the graviton were to have a mass? Static black hole solutions in massive gravity appear to unavoidably suffer from either infinite strong coupling at all scales or coordinate-invariant curvature singularities at the horizon. (See, e.g., [1,2,3] for specific arguments.) In [2,3] it was argued that these pathologies can be avoided by adopting a time-dependent, spherically symmetric ansatz
Perturbative time-dependent solutions were found in [3] which are regular at the horizon, are potentially consistent with the expected Yukawa asymptotics at large distances and weak coupling, and possess a massless limit that smoothly recovers the Schwarzschild black holes of general relativity
We are primarily interested in the laws of black hole mechanics [4] in the presence of a graviton mass
Summary
It remains an open question: what would happen to a black hole if the graviton were to have a mass? Static black hole solutions in massive gravity appear to unavoidably suffer from either infinite strong coupling at all scales or coordinate-invariant curvature singularities at the horizon. (See, e.g., [1,2,3] for specific arguments.) In [2,3] it was argued that these pathologies can be avoided by adopting a time-dependent, spherically symmetric ansatz. Generic theories of massive gravitons require a fiducial reference metric fμν in addition to the dynamical metric gμν in order to construct nonderivative potential terms. We derive several additional consequences of this initial assumption: the apparent horizon is a null surface in terms of the dynamical metric; the surface gravity can be computed in terms of the inaffinity of the Kodama vector at the horizon; and the area of the apparent horizon is never decreasing, consistent with a second law of black hole mechanics. We find solutions consistent both with the assumption of a null apparent horizon and that have a time-independent surface gravity. These solutions are truly time-dependent in that they possess no timelike Killing vector. We compute the time-dependent scalar curvature at the horizon and discuss some implications
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
