Scalar-tensor gravity and conformal continuations

Global properties of vacuum static, spherically symmetric configurations are studied in a general class of scalar-tensor theories (STTs) of gravity in various dimensions. The conformal mapping between the Jordan and Einstein frames is used as a tool. Necessary and sufficient conditions are found for the existence of solutions admitting a conformal continuation (CC). The latter means that a singularity in the Einstein-frame manifold maps to a regular surface Strans in the Jordan frame, and the solution is then continued beyond this surface. Strans can be an ordinary regular sphere or a horizon. In the second case, Strans connect two epochs of a Kantowski-Sachs type cosmology. It is shown that the list of possible types of global causal structure of vacuum space-times in any STT, with any potential function U(φ), is the same as in general relativity with a cosmological constant. This is even true for conformally continued solutions. A traversable wormhole is shown to be one of the generic structures created as a result of CC. Two explicit examples are presented: the known solution for a conformal field in general relativity, illustrating the emergence of singularities and wormholes due to CC, and a nonsingular three-dimensional model with an infinite sequence of CCs. © 2002 American Institute of Physics.