A family of solutions to the inverse problem in gravitation: building a theory around a metric
Arthur G. Suvorov
Abstract
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.
Topics & Concepts
PhysicsGravitationMetric (unit)SpacetimeParameterized complexityScalar–tensor theoryDifferential geometryMetric tensorScalar (mathematics)Classical mechanicsTheoretical physicsKerr metricEquations of motionMathematical analysisGeometryMathematicsSchwarzschild radiusQuantum mechanicsGeodesicAlgorithmEconomicsOperations managementCosmology and Gravitation TheoriesBlack Holes and Theoretical PhysicsAdvanced Differential Geometry Research