Analytic solutions in non-linear massive gravity

TL;DR

A spherically symmetric solutions in a covariant massive gravity model, which is a candidate for a ghost-free nonlinear completion of the Fierz-Pauli theory, is studied.

Abstract

We study spherically symmetric solutions in a covariant massive gravity model, which is a candidate for a ghost-free non-linear completion of the Fierz-Pauli theory. There is a branch of solutions that exhibits the Vainshtein mechanism, recovering General Relativity below a Vainshtein radius given by $(r_g m^2)^{1/3}$, where $m$ is the graviton mass and $r_g$ is the Schwarzschild radius of a matter source. Another branch of exact solutions exists, corresponding to Schwarzschild-de Sitter spacetimes where the curvature scale of de Sitter space is proportional to the mass squared of the graviton.

Figures (1)

• Figure 1: Numerical solution for $\partial_r\tilde{f}=\tilde{f}'$, $\partial_r n=n'$, and the quotient $\gamma'\equiv\tilde{f'}/2n'$ around the Vainshtein radius $\rho_v$ (left) and the Compton Wavelength $\rho\sim 1/m$ (right). Region 1 (2) shows how GR solutions are (not) recovered inside (outside) the Vainshtein radius $\rho_V$. Region 3 shows the asymptotic decay of the linear solutions (Eq. (\ref{['linsol']})). Here, $GM=1$.