Gravitational self-force in scalar-tensor gravity

Motivated by the theoretical possibility of floating orbits and the potential to contribute 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 space-time 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 space-time in general relativity, with both falling under the general class of hyperbolic field equations studied in. Here, we solve the field equations formally in terms of retarded Green functions, which have explicit representations as Hadamard forms in the neighborhood of the world line. To compute the equation of motion, we parametrize the world line by the particle's mass and "charge," which we define in terms of the original Jordan frame mass, its derivative, and the parameter which translates the proper time in the Jordan frame to the Einstein frame.