Generalized theories of gravity and conformal continuations
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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 S_trans 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 S_trans is an ordinary regular sphere and when it is a Killing horizon. Two explicit examples of CCs are presented.
5 pages, contribution to Proc. of 12th Russian Grav. Conf., Kazan, 20-26 June 2005. References updated
5 pages, contribution to Proc. of 12th Russian Grav. Conf., Kazan, 20-26 June 2005. References updated