A family of solutions to the inverse problem in gravitation: building a theory around a metric

Abstract

A method is presented to construct a particular, non-minimally coupled scalar-tensor theory such that a given metric is an exact vacuum solution in that theory. In contrast to the standard approach in studies of gravitational dynamics, where one begins with an action and then solves the equations of motion, this approach allows for an explicit theory to be built around some pre-specified geometry. Starting from a parameterized black hole spacetime with generic, non-Kerr hairs, it is shown how an overarching family of theories can be designed to fit the metric exactly.

5 pages, 1 figure, substantially revised. Accepted for publication in Gen. Rel. Grav. Lett

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• A Critical Assessment of Black Hole Solutions With a Linear Term in Their Redshift Function
• Resonant excitation of eccentricity in spherical extreme-mass-ratio inspirals
• Taxonomy of periodic orbits and gravitational waves in a non-rotating Destounis-Suvorov-Kokkotas black hole spacetime
• General Framework for the Spontaneous Scalarization of Regular Black Holes
• Confronting eikonal and post-Kerr methods with numerical evolution of scalar field perturbations in spacetimes beyond Kerr