Spherically symmetric solutions of light Galileon

Abstract

We have been studied the model of light Galileon with translational shift symmetry $\varphi \to \varphi +c$. The matter Lagrangian is presented in the form ${\mathcal{L}}_{\varphi }=-\eta (\partial \varphi {)}^2+\beta G^{\mu \nu }{\partial }_{\mu }\varphi {\partial }_{\nu }\varphi$. 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 $\varphi =t$, which it is remembered by us dilaton field.

Accepted in "International Journal of Theoretical Physics"

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• Off-shell Noether current and conserved charge in Horndeski theory
• Galileons, phantom fields, and the fate of the Universe
• Compact Stars in Vector-Tensor-Horndeski Theory of Gravity
• Scalar-tensor black holes in an expanding universe