Non linear massive gravity as a gravitational $\sigma$-model

Abstract

We show the direct analogy between the ghost-free non-linear formulation of massive gravity and the standard $\sigma$-models well understood in the literature. This issue explains why there are two non-trivial family of solutions for the spherically symmetric case inside the non-linear massive gravity formulations with two free-parameters $\alpha$ and $\beta$. In general, the case $\beta <{\alpha }^2$ has a single physical vacuum state. On the other hand, the case $\beta ={\alpha }^2$ contains a natural vacuum degeneracy. This is in perfect analogy with the $\sigma$-model for scalar fields where depending on the values taken by the parameters of the theory the vacuum can be single or degenerate.

Journal (Published) version up to some final edition arrangements, 5 pages, references added, one section added

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Cited by in corpus (6)

• On a model of magnetically charged black hole with nonlinear electrodynamics
• The effects of massive graviton on the equilibrium between the black hole and radiation gas in an isolated box
• Decaying dark energy in light of the latest cosmological dataset
• Gauge symmetries and the Higgs mechanism in Quantum Finance
• Vacuum degeneracy in Massive gravity=Multiplicity of fundamental scales
• The dynamical origin of the graviton mass in the non-linear theory of massive gravity