Abstract
We review properties of solutions in bigravity theory for a specific case where two metric tensors, \(g_{\mu \nu}\) and \(f_{\mu \nu}\), satisfy proportional relation \(f_{\mu \nu}=C^{2}g_{\mu \nu}\). For this condition, we find that the solutions describing the asymptotically de Sitter space-time can be obtained and investigate the perturbation around the Schwarzschild–de Sitter solutions and corresponding anti-evaporation. We discuss the stability under special perturbations related to the anti-evaporation and the importance of the non-diagonal components of the metric in bigravity.
Highlights
Much attention has been paid to bigravity theory [1,2], which includes two independent metric tensor fields, gμν and fμν
Bigravity contains a massive spin-2 propagating mode in addition to the ordinary massless spin-2 graviton, and it has been successfully constructed as the generalization of de Rham–Gabadadze–Tolley massive gravity [3,4,5], which describes a ghost-free massive spin-2 field theory
When we extend the theory to make both of the two metrics dynamical, the bigravity theory can be obtained [1,2]
Summary
Much attention has been paid to bigravity theory [1,2], which includes two independent metric tensor fields, gμν and fμν. The theory describing the interaction between two spin-2 fields, where one field is massless and another should be massive, is called bi-metric or bigravity theory. This theory was probably first proposed by Rosen [15,16,17] and had been studied as f-g gravity or strong gravity theory [18,19,20]. The ghost-free interaction between massless and massive spin-2 fields was established as a generalization of ghost-free massive spin-2 field theory, that is the dRGT massive gravity. I review some properties of a special class of solutions in bigravity [42] and show that the specific family of Schwarzschild–de Sitter is stable for a special class of perturbation [43]
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