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.

27 pages, no figures. Current version: fixed typos, added DOI

References in corpus (26)

• The Confrontation between General Relativity and Experiment
• Resummation of Massive Gravity
• Interacting Spin-2 Fields
• Thermodynamics of Black Holes in Massive Gravity
• Black holes as particle detectors: evolution of superradiant instabilities
• Massive gravity: nonlinear instability of the homogeneous and isotropic universe
• P-V criticality in the extended phase space of black holes in massive gravity
• A Clockwork Theory
• Exact Schwarzschild-de Sitter black holes in a family of massive gravity models
• On couplings to matter in massive (bi-)gravity
• The recovery of General Relativity in massive gravity via the Vainshtein mechanism
• Ghosts & Matter Couplings in Massive (bi-&multi-)Gravity
• Heavy spin-2 Dark Matter
• Viable cosmology in bimetric theory
• Oscillating Spin-2 Dark Matter
• No-Go Theorems for Unitary and Interacting Partially Massless Spin-Two Fields
• The coupling to matter in Massive, Bi- and Multi-Gravity
• The Vainshtein mechanism in the Decoupling Limit of massive gravity
• A class of charged black hole solutions in massive (bi)gravity
• Hawking-Page transition in holographic massive gravity
• Appearance of Boulware-Deser ghost in bigravity with doubly coupled matter
• Rotating black holes in massive gravity
• AdS/Ricci-flat correspondence and the Gregory-Laflamme instability
• A non-linear extension of the spin-2 partially massless symmetry
• Cycles of interactions in multi-gravity theories
• Instability and backreaction of massive spin-2 fields around black holes

Cited by in corpus (4)

• Mass spectrum and linear perturbations of ghost-free multi-spin-2 theory
• Black Holes in Multi-Metric Gravity II: Hairy Solutions and Linear Stability of the Non- and Partially Proportional Branches
• Gravitational wave propagation in bigravity in the late universe
• Dipolar perturbations of nonbidiagonal black holes in bigravity