Spacetime symmetries and topology in bimetric relativity

Abstract

We explore spacetime symmetries and topologies of the two metric sectors in Hassan-Rosen bimetric theory. We show that, in vacuum, the two sectors can either share or have separate spacetime symmetries. If stress-energy tensors are present, a third case can arise, with different spacetime symmetries within the same sector. This raises the question of the best definition of spacetime symmetry in Hassan-Rosen bimetric theory. We emphasize the possibility of imposing ansätze and looking for solutions having different Killing vector fields or different isometries in the two sectors, which has gained little attention so far. We also point out that the topology of spacetime imposes a constraint on possible metric combinations.

arXiv comment19 pages. It matches with the published version. Comments are welcome. Attached Mathematica notebook available in the ancillary files and at https://tinyurl.com/y9r7nuuh

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• Covariant BSSN formulation in bimetric relativity
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• The mean gauges in bimetric relativity
• Gravitational-wave energy and other fluxes in ghost-free bigravity
• Analytical constraints on bimetric gravity
• Generalized Vaidya solutions in bimetric gravity
• Dipolar perturbations of nonbidiagonal black holes in bigravity