A combined Majumdar-Papapetrou-Bonnor field as extreme limit of the double-Reissner-Nordstrom solution

TL;DR

This paper derives an explicit analytical form of a combined extremal electromagnetic field, unifying known solutions and describing a pair of non-rotating extremal black holes with unequal masses and charges.

Contribution

It introduces the combined Majumdar-Papapetrou-Bonnor field as a new explicit solution encompassing previous special cases.

Findings

Provides explicit analytical form in prolate spheroidal coordinates.

Interprets the solution as a pair of extremal black holes with specific charge-mass relations.

Unifies two known electrostatic solutions into a single framework.

Abstract

The general extreme limit of the double-Reissner-Nordstrom solution is worked out in explicit analytical form involving prolate spheroidal coordinates. We name it the combined Majumdar-Papapetrou-Bonnor field to underline the fact that it contains as particular cases the two-body specialization of the well-known Majumdar-Papapetrou solution and Bonnor's three-parameter electrostatic field. To the latter we give a precise physical interpretation as describing a pair of non-rotating extremal black holes with unequal masses and unequal opposite charges kept apart by a strut, the absolute values of charges exceeding the respective (positive) values of masses.