Stationary black holes with stringy hair

TL;DR

This paper explores black holes pierced by cosmic strings, introducing a stringy matter model, deriving solutions for static and rotating black holes, and analyzing the effects of stringy matter on black hole properties and spacetime geometry.

Contribution

It presents a new solution for charged static black holes with stringy matter and analyzes test strings in rotating black hole spacetimes, linking string configurations to black hole characteristics.

Findings

Derived a static black hole solution with stringy matter and cosmological constant.

Calculated stress-energy tensor for strings in Kerr and Kerr-NUT-(A)dS geometries.

Discussed angular momentum extraction by strings from rotating black holes.

Abstract

We discuss properties of black holes which are pierced by special configurations of cosmic strings. For static black holes we consider radial strings in the limit when the number of strings grows to infinity while the tension of each single string tends to zero. In a properly taken limit the stress-energy tensor of the string distribution is finite. We call such matter stringy matter. We present a solution of the Einstein equations for an electrically charged static black hole with the stringy matter, with and without cosmological constant. This solution is a warped product of two metrics. One of them is a deformed two-sphere whose Gaussian curvature is determined by the energy-density of the stringy matter. We discuss the embedding of a corresponding distorted sphere into a three-dimensional Euclidean space and formulate consistency conditions. We also found a relation between the square of the Weyl tensor invariant of the four dimensional spacetime of the stringy black holes and the energy density of the stringy matter. In the second part of the paper, we discuss test stationary strings in the Kerr geometry and in its Kerr-NUT-(A)dS generalizations. Explicit solutions for strings that are regular at the event horizon are obtained. Using these solutions the stress-energy tensor of the stringy matter in these geometries is calculated. Extraction of the angular momentum from rotating black holes by such strings is also discussed.