Gravitational self-force in scalar-tensor gravity

Understand

Motivated by the discovery of floating orbits and the potential to provide extra constraints on alternative theories, in this paper we derive the self-force equation for a small compact object moving on an accelerated world line in a background spacetime which is a solution of the coupled gravitational and scalar field equations of scalar-tensor theory.

• In the Einstein frame, the coupled field equations governing the perturbations sourced by the particle share the same form as the field equations for perturbations of a scalarvac spacetime, with both falling under the general class of hyperbolic field equations studied by Zimmerman and Poisson.
• Here, we solve the field equations formally in terms of retarded Green functions, which have explicit representations as Hadamard forms in the neighbourhood of the world line.
• Using a quasi-local expansion of the Hadamard form, we derive the regular solutions in Fermi normal coordinates according to the Detweiler-Whiting prescription.