Spherically symmetric solutions of light Galileon

TL;DR

This paper explores spherically symmetric solutions in a light Galileon model with shift symmetry, showing its relation to modified gravity and presenting an exact solution with specific singularity and current properties.

Contribution

It demonstrates that light Galileons are related to modified gravity models and provides an exact spherically symmetric solution with unique properties.

Findings

Found an exact spherically symmetric solution with a singularity at r=0.

Proved the solution has a non-divergent current vector norm.

Linked the model to f(R,R^{μν}T_{μν}) gravity.

Abstract

We have been studied the model of light Galileon with translational shift symmetry $\phi\to \phi+c$. The matter Lagrangian is presented in the form $\mathcal{L}_{\phi}= -\eta (\partial \phi)^2+\beta G^{\mu\nu}\partial_{\mu}\phi\partial_{\nu}\phi$. We have been addressed two issues: the first is that, we have been proven that, this type of Galileons belong to the modified matter-curvature models of gravity in type of $f(R,R^{\mu\nu}T_{\mu\nu}^m)$. Secondly, we have been investigated exact solution for spherically symmetric geometries in this model. We have been found an exact solution with singularity at $r=0$ in null coordinates. We have been proven that the solution has also a non-divergence current vector norm. This solution can be considered as an special solution which has been investigated in literature before, in which the Galileon's field is non-static (time dependence). Our scalar-shift symmetrized Galileon has the simple form of $\phi=t$, which it is remembered by us dilaton field.