On the electrogravity-dual solution to stringy charged black holes

Abstract

By resolving the Riemann curvature tensor relative to a timelike unit vector into electric and magnetic parts, electrogravity-duality transformation is defined. Such a transformation interchanges the "active" and "passive" electric parts of this tensor and can be used to obtain spacetime metrics dual to known solutions of any geometric theory of gravity, such as Einstein gravity. The vacuum field equations of general relativity are invariant under such a transformation. It is possible to break this symmetry by introducing matter terms in such a way that the characteristic vacuum solution is still obtained as a special case of that matter distribution. Such a possibility exists for all stationary black hole solutions. Interestingly, solutions exist even for the dual equations with the matter terms. Here, we extend this formalism to study the static, charged black hole solutions of a four-dimensional low-energy effective action of heterotic string theory. We show that analogous to general relativity, the dual solution is itself a similar black hole spacetime, endowed with a global monopole charge.