We study the problem of a four-dimensional brane lying in the five-dimensional degenerate Schwarzschild–de Sitter (Nariai) black hole in five-dimensional $F(R)$ gravity. We show that there cannot exist the brane in the Nariai bulk space except for the case where the brane tension vanishes. We demonstrate that the five-dimensional Nariai bulk is unstable in a large region of the parameter space. In particular, the Nariai bulk can have classical (anti)evaporation instabilities. The bulk instability backreacts on the four-dimensional brane, in that case, the brane tension vanishes, and the unstable modes propagate in their world volume.

• Received 15 December 2016

DOI:https://doi.org/10.1103/PhysRevD.95.124020