Spherically Symmetric Solutions of Light Galileon

Abstract

We have been studied the model of light Galileon with translational shift symmetry φ → φ + c. The matter Lagrangian is presented in the form Lφ = −η(∂φ)2 + βGμν ∂μφ∂νφ. 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, RμνT m μν ). 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 φ = t, which it is remembered by us dilaton field.