Topological classes of higher-dimensional black holes in massive gravity

In this paper, we study topological numbers for five-, six- and seven-dimensional anti-de Sitter black holes in the ghost-free massive gravity. We find that when the black holes are charged, they have the same topological number. The topological numbers for the uncharged black holes are 0 or 1, and the specific values are determined by the values of the black holes ' parameters. Since k and c(0)(2)c(2)m(2) appear together in the generalized free energy in the form of k + c(0)(2)c(2)m(2,) where k characterizes the horizon curvature and c(2)m(2) is the coefficient of the second term of massive potential associated with the gravitonmass, this result is applicable to the black holes with the spherical, Ricci flat or hyperbolic horizons. This work shows that the parameters of the ghostfree massive gravity play an important role in topological classes of black holes.

Automated summary

In this paper, topological numbers for five-, six- and seven-dimensional anti-de Sitter black holes in the ghost-free massive gravity are studied. It is found that charged black holes have the same topological number. The topological numbers for uncharged black holes are either 0 or 1, with specific values determined by the parameters of the black holes. This work demonstrates the important role of the parameters of the ghost-free massive gravity in the topological classes of black holes.