Vaidya solution and its generalization in de Rham-Gabadadze-Tolley massive gravity

TL;DR

This paper explores the Vaidya solution and its generalizations within de Rham-Gabadadze-Tolley massive gravity, revealing new black hole solutions with variable horizons through nonunitary gauge ansatz.

Contribution

It introduces new Vaidya-type solutions in dRGT massive gravity using nonunitary gauge ansatz, expanding the understanding of black hole solutions in this theory.

Findings

Derived three types of Vaidya solutions with nonunitary gauge

Found generalized and furry Vaidya solutions in dRGT gravity

Obtained series of furry black hole solutions

Abstract

We present a detailed study of the Vaidya solution and its generalization in de Rham-Gabadadze-Tolley (dRGT) theory. Since the diffeomorphism invariance can be restored with the St\"{u}ckelberg fields $\phi^a$ introduced, there is a new invariant $I^{ab}=g^{\mu \nu}\partial_\mu \phi^a\partial_\nu \phi^b$ in the massive gravity, which adds to the ones usually encountered in general relativity. There is no conventional Vaidya solution if we choose unitary gauge. In this paper, we obtain three types of self-consistent ansatz with some nonunitary gauge, and find accordingly the Vaidya, generalized Vaidya and furry Vaidya solution. As by-products, we obtain a series of furry black hole. The Vaidya solution and its generalization in dRGT massive gravity describe the black holes with a variable horizon.