On geometry of deformed black holes: I. Majumdar-Papapetrou binary

TL;DR

This paper investigates how the presence of additional bodies, especially another black hole, influences the geometry around black holes using exact solutions of Einstein's equations, focusing on the Majumdar-Papapetrou binary system.

Contribution

It provides a detailed analysis of space-time deformation around binary black holes, emphasizing the effects of nearby bodies on curvature invariants in static, axially symmetric configurations.

Findings

Black hole geometry is significantly affected by nearby black holes.

Deformation due to other black holes can be compared to rotational effects in Kerr solutions.

Level surfaces of invariants reveal strong influences near singularities.

Abstract

Although black holes are eminent manifestations of very strong gravity, the geometry of space-time around and even inside them can be significantly affected by additional bodies present in their surroundings. We study such an influence within static and axially symmetric (electro-)vacuum space-times described by exact solutions of Einstein's equations, considering astrophysically motivated configurations (such as black holes surrounded by rings) as well as those of pure academic interest (such as specifically "tuned" systems of multiple black holes). The geometry is represented by the simplest invariants determined by the metric (the lapse function) and its gradient (gravitational acceleration), with special emphasis given to curvature (the Kretschmann and Ricci-square scalars). These quantities are analyzed and their level surfaces plotted both above and below the black-hole horizons, in particular near the central singularities. Estimating that the black hole could be most strongly affected by the other black hole, we focus, in this first paper, on the Majumdar--Papapetrou solution for a binary black hole and compare the deformation caused by "the other" hole (and the electrostatic field) with that induced by rotational dragging in the well-known Kerr and Kerr--Newman solutions.