Scalar-tensor gravity and conformal continuations

TL;DR

This paper investigates the global properties of vacuum static, spherically symmetric solutions in scalar-tensor theories of gravity, focusing on conformal continuations that relate singularities and regular surfaces across different conformal frames.

Contribution

It establishes necessary and sufficient conditions for conformal continuations in scalar-tensor gravity and explores their implications for causal structures and wormhole formation.

Findings

Conformal continuations can connect singularities to regular surfaces, including horizons and wormholes.

The causal structure of vacuum solutions in scalar-tensor theories matches that of general relativity with a cosmological constant.

Explicit examples demonstrate both the emergence of wormholes and models with infinite conformal continuations.

Abstract

Global properties of vacuum static, spherically symmetric configurations are studied in a general class of scalar-tensor theories (STT) 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 S_(trans) in the Jordan frame, and the solution is then continued beyond this surface. S_(trans) can be an ordinary regular sphere or a horizon. In the second case, S_(trans) proves to connect two epochs of a Kantowski-Sachs type cosmology. It is shown that, in an arbitrary STT, with arbitrary potential functions $U(\phi)$, the list of possible types of causal structures of vacuum space-times is the same as in general relativity with a cosmological constant. This is true even for conformally continued solutions. It is found that when S_(trans) is an ordinary sphere, one of the generic structures appearing as a result of CC is a traversable wormhole. Two explicit examples are presented: a known solution illustrating the emergence of singularities and wormholes, and a nonsingular 3-dimensional model with an infinite sequence of CCs.