The electrogravity transformation and global monopoles in scalar-tensor gravity

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. Pacs: 04.20.Jb, 04.70.Bw, 11.27.+d, 98.80.Cq Typeset using REVTEX ∗Electronic address: [email protected] †Electronic address: [email protected]