Stealth configurations in vector-tensor theories of gravity

TL;DR

This paper explores stealth solutions in vector-tensor gravity theories, revealing configurations where the geometry mimics Einstein gravity but includes non-trivial vector fields, aiding the understanding of compact objects in modified gravity.

Contribution

It introduces new spherically symmetric and slowly rotating solutions in vector-tensor Galileon theories with symmetries that prevent vector polarization propagation, including stealth configurations with Einstein-like geometry.

Findings

Existence of stealth solutions with Einstein geometry and non-trivial vector fields.

Stealth configurations extend to asymptotic infinity with independent parameters.

Implications for modeling black holes and neutron stars in modified gravity.

Abstract

Studying the physics of compact objects in modified theories of gravity is important for understanding how future observations can test alternatives to General Relativity. We consider a subset of vector-tensor Galileon theories of gravity characterized by new symmetries, which can prevent the propagation of the vector longitudinal polarization, even in absence of Abelian gauge invariance. We investigate new spherically symmetric and slowly rotating solutions for these systems, including an arbitrary matter Lagrangian. We show that, under certain conditions, there always exist stealth configurations whose geometry coincides with solutions of Einstein gravity coupled with the additional matter. Such solutions have a non-trivial profile for the vector field, characterized by independent integration constants, which extends to asymptotic infinity. We interpret our findings in terms of the symmetries and features of the original vector-tensor action, and on the number of degrees of freedom that it propagates. These results are important to eventually describe gravitationally bound configurations in modified theories of gravity, such as black holes and neutron stars, including realistic matter fields forming or surrounding the object.