Generalized theories of gravity and conformal continuations

الأصل · EN

Many theories of gravity admit formulations in different, conformally related manifolds, known as the Jordan and Einstein conformal frames. Among them are various scalar-tensor theories of gravity and high-order theories with the Lagrangian f(R) where R is the scalar curvature and f an arbitrary function. It may happen that a singularity in the Einstein frame corresponds to a regular surface Sₜrans in the Jordan frame, and the space-time is then continued beyond this surface. This phenomenon is called a conformal continuation (CC). We discuss the properties of vacuum static, spherically symmetric configurations of arbitrary dimension in scalar-tensor and f(R) theories of gravity and indicate necessary and sufficient conditions for the existence of solutions admitting a CC. Two cases are distinguished, when Sₜrans is an ordinary regular sphere and when it is a Killing horizon. Two explicit examples of CCs are presented.