Black Holes in Multi-Metric Gravity

Abstract: We construct a wide class of black hole solutions to the general theory of ghost free multi-metric gravity in arbitrary spacetime dimension, extending and generalising the known results in 4-dimensional dRGT massive gravity and bigravity. The solutions are split into three generic classes based on whether the metrics can be simultaneously diagonalised - one of which does not exist in dRGT massive gravity nor bigravity, and is only possible when one has more than two interacting metric fields. We also linearise the general multi-metric theory to determine the dynamics of the massive spin-2 modes, including examples where this can be done analytically, and use the linear theory to discuss the stability of the 4-dimensional multi-Schwarzchild and multi-Kerr solutions. We explain how the instabilities that plague these solutions in dRGT massive gravity and bigravity carry across to the general multi-metric theory, touching upon ideas of dimensional deconstruction to make sense of the results.