Generalized Vaidya Solutions and Misner-Sharp mass for $n$-dimensional massive gravity

Abstract

Dynamical solutions are always of interest to people in gravity theories. We derive a series of generalized Vaidya solutions in the $n$-dimensional de Rham-Gabadadze-Tolley (dRGT) massive gravity with a singular reference metric. Similar to the case of the Einstein gravity, the generalized Vaidya solution can describe shining/absorbing stars. Moreover, we also find a more general Vaidya-like solution by introducing a more generic matter field than the pure radiation in the original Vaidya spacetime. As a result, the above generalized Vaidya solution is naturally included in this Vaidya-like solution as a special case. We investigate the thermodynamics for this Vaidya-like spacetime by using the unified first law, and present the generalized Misner-Sharp mass. Our results show that the generalized Minser-Sharp mass does exist in this spacetime. In addition, the usual Clausius relation $\delta Q=TdS$ holds on the apparent horizon, which implicates that the massive gravity is in a thermodynamic equilibrium state. We find that the work density vanishes for the generalized Vaidya solution, while it appears in the more general Vaidya-like solution. Furthermore, the covariant generalized Minser-Sharp mass in the $n$-dimensional de Rham-Gabadadze-Tolley massive gravity is also derived by taking a general metric ansatz into account.

10 pages, no figure, version published in PRD

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• Holographic conductivity in the massive gravity with power-law Maxwell field
• Greybody factor for massive fermion emitted by a black hole in dRGT massive gravity theory
• Quasinormal Modes for Dynamical Black Holes
• Quasinormal modes of a massless Dirac field in de Rham-Gabadadze-Tolley massive gravity
• Rotating black string in dRGT massive gravity
• The effects of massive graviton on the equilibrium between the black hole and radiation gas in an isolated box
• Equation of State and Joule-Thomson Expansion for the FRW Universe in the Brane World Scenario
• GEMS embeddings and freely falling temperatures of Schwarzschild(-AdS) black holes in massive gravity
• Thermodynamics of Black String from Rényi entropy in de Rham-Gabadadze-Tolley Massive Gravity Theory
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• Towards a sound massive cosmology
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• GEMS embeddings of Hayward regular black holes in massless and massive gravities