Black hole mechanics for massive gravitons

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 there is a natural sense in which the locati...

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Bibliographic Details
Published in:Physical review. D 2018-11, Vol.98 (10), p.104008, Article 104008
Main Author: Rosen, Rachel A.
Format: Article
Language:English
Subjects:
Black holes
Curvature
Gravitation
Gravitons
Mathematical models
Mechanics
Mechanics (physics)
Time dependence
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Summary: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 there is a natural sense in which the location of the horizon is necessarily time-independent, despite the dynamical metric possessing no time-like Killing vector. 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. These results are nonperturbative and model-independent. 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.
ISSN:2470-0010
2470-0029
DOI:10.1103/PhysRevD.98.104008