Analogs of the double-Reissner-Nordstrom solution in magnetostatics and dilaton gravity: mathematical description and some physical properties

TL;DR

This paper constructs magnetic analogs of the double-Reissner-Nordstrom solution, explores their properties under transformations, and generalizes them to dilaton gravity, revealing simple formulas for horizon areas and surface gravities.

Contribution

It introduces explicit magnetic potential solutions, identifies conditions for equilibrium black diholes, and extends the solutions to dilaton gravity with new physical insights.

Findings

Explicit magnetic potential for double-Reissner-Nordstrom analogs

Conditions for equilibrium of asymmetric black diholes

Simple formulas for horizon areas and surface gravities

Abstract

In this paper we consider a magnetic analog of the double-Reissner-Nordstrom solution and construct the corresponding magnetic potential A_\varphi in the explicit form. The behavior of the resulting solution under the Harrison transformation then naturally singles out the asymmetric black diholes - configurations composed of two non-extreme black holes possessing unequal masses, and charges equal in magnitude but opposite in sign - as its most general subclass for which equilibrium of the black-hole constituents can be achieved with the aid of the external magnetic (or electric) field. We also generalize the double-Reissner-Nordstrom solution to the dilaton gravity with arbitrary dilaton coupling, yielding as the result the 4-dimensional double-Gibbons-Maeda spacetime. The study of some physical properties of the solutions obtained leads, in particular, to very simple formulas for the areas of the horizons and surface gravities.