Exact Solutions in Massive Gravity

Abstract

Massive gravity is a good theoretical laboratory to study modifications of General Relativity. The theory offers a concrete set-up to study models of dark energy, since it admits cosmological self-accelerating solutions in the vacuum, in which the size of the acceleration depends on the graviton mass. Moreover, non-linear gravitational self-interactions, in the proximity of a matter source, manage to mimic the predictions of linearised General Relativity, hence agreeing with solar-system precision measurements. In this article, we review our work in the subject, classifying, on one hand, static solutions, and on the other hand, self-accelerating backgrounds. For what respects static solutions we exhibit black hole configurations, together with other solutions that recover General Relativity near a source via the Vainshtein mechanism. For the self-accelerating solutions we describe a wide class of cosmological backgrounds, including an analysis of their stability.

17 pages, 4 figures. Invited review to CQG focus issue on massive gravity

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• Cosmological dynamics and dark energy from non-local infrared modifications of gravity
• A class of charged black hole solutions in massive (bi)gravity
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• Mixed Galileons and Spherically Symmetric Solutions
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• Stable FLRW solutions in Generalized Massive Gravity
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• Non-Singular Black Holes in Massive Gravity: Time-Dependent Solutions
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• Interacting spin-2 fields in the Stueckelberg picture
• Quasi Normal Modes and P-V Criticallity for scalar perturbations in a class of dRGT massive gravity around Black Holes
• Generalized Vaidya Solutions and Misner-Sharp mass for $n$-dimensional massive gravity
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• New Branches of Massive Gravity
• Rotating black string in dRGT massive gravity
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• Entropy spectrum of charged BTZ black holes in massive gravity's rainbow
• Translation invariant time-dependent solutions to massive gravity II
• Cosmological evolutions of $F(R)$ nonlinear massive gravity
• Conformal couplings of Galileons to other degrees of freedom
• Beyond self-acceleration: force- and fluid-acceleration
• Effective Matter Cosmologies of Massive Gravity: Physical Fluids
• Fundamental fields around compact objects: Massive spin-2 fields, Superradiant instabilities and Stars with dark matter cores
• Milgrom's Law and Lambda's Shadow: How Massive Gravity Connects Galactic and Cosmic Dynamics