The electrogravity transformation and global monopoles in scalar-tensor gravity

TL;DR

This paper extends the electrogravity transformation to scalar-tensor gravity theories, deriving dual solutions that incorporate global monopole charges, thus broadening the understanding of dualities in alternative gravity models.

Contribution

It generalizes the electrogravity transformation to scalar-tensor theories, providing new dual solutions with monopole charges in these frameworks.

Findings

Dual solutions in scalar-tensor theories include global monopole charges.

The formalism applies to both black hole and naked singularity solutions.

Dual solutions resemble original spacetimes with added monopole features.

Abstract

The electrogravity transformation is defined by an interchange of the ``active'' and ``passive'' electric parts of the Riemann tensor. Such a transformation has been used to find new solutions that are ``dual'' to the Kerr family of black hole spacetimes in general relativity. In such a case, the dual solution is a similar black hole spacetime endowed with a global monopole charge. Here, we extend this formalism to obtain solutions dual to the static, spherically symmetric solutions of two different scalar-tensor gravity theories. In particular, we first study the duals of the charged black hole solutions of a four-dimensional low-energy effective action of heterotic string theory. Next, we study dual of the Xanthopoulos-Zannias solution in Brans-Dicke theory, which contains a naked singularity. We show that, analogous to general relativity, in these scalar-tensor gravity theories the dual solutions are similar to the original spacetimes, but with a global monopole charge.