Characterising Vainshtein Solutions in Massive Gravity

Abstract

We study static, spherically symmetric solutions in a recently proposed ghost-free model of non-linear massive gravity. We focus on a branch of solutions where the helicity-0 mode can be strongly coupled within certain radial regions, giving rise to the Vainshtein effect. We truncate the analysis to scales below the gravitational Compton wavelength, and consider the weak field limit for the gravitational potentials, while keeping all non-linearities of the helicity-0 mode. We determine analytically the number and properties of local solutions which exist asymptotically on large scales, and of local (inner) solutions which exist on small scales. We find two kinds of asymptotic solutions, one of which is asymptotically flat, while the other one is not, and also two types of inner solutions, one of which displays the Vainshtein mechanism, while the other exhibits a self-shielding behaviour of the gravitational field. We analyse in detail in which cases the solutions match in an intermediate region. The asymptotically flat solutions connect only to inner configurations displaying the Vainshtein mechanism, while the non asymptotically flat solutions can connect with both kinds of inner solutions. We show furthermore that there are some regions in the parameter space where global solutions do not exist, and characterise precisely in which regions of the phase space the Vainshtein mechanism takes place.

21 pages, 7 figures, published version

References in corpus (14)

• Resummation of Massive Gravity
• Confirmation of the Secondary Constraint and Absence of Ghost in Massive Gravity and Bimetric Gravity
• Cosmic Acceleration and the Helicity-0 Graviton
• Open FRW universes and self-acceleration from nonlinear massive gravity
• Exact Schwarzschild-de Sitter black holes in a family of massive gravity models
• Vainshtein screening in a cosmological background in the most general second-order scalar-tensor theory
• Cosmological perturbations of self-accelerating universe in nonlinear massive gravity
• On Black Holes in Massive Gravity
• The recovery of General Relativity in massive gravity via the Vainshtein mechanism
• Hairy black holes in the ghost-free bigravity theory
• Spherically Symmetric Solutions in Ghost-Free Massive Gravity
• Vainshtein mechanism in second-order scalar-tensor theories
• The Self-Accelerating Universe with Vectors in Massive Gravity
• Spherically Symmetric Solutions in Massive Gravity and Constraints from Galaxies

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