On the nature of cosmic strings in black hole spacetimes

TL;DR

This paper introduces a new model for cosmic strings attached to black holes, revealing their stress-energy tensor involves derivatives of delta functions and demonstrating their role in black hole acceleration and gravitational radiation.

Contribution

It provides an explicit construction of cosmic strings in black hole spacetimes using a limiting process from the Bonnor rocket, highlighting their unique stress-energy properties and physical effects.

Findings

Cosmic strings can be modeled as conical singularities with derivative delta function stress-energy.

The constructed solutions include Schwarzschild and C-metric with cosmic strings.

Cosmic strings induce momentum flux causing black hole acceleration, consistent with gravitational radiation.

Abstract

A new model for cosmic strings (i.e. conical singularities) attached to black holes is proposed. These string are obtained by a explicit construction via limiting process from the so-called Bonnor rocket. This reveals quite surprising nature of their stress-energy tensor which contains first derivative of Dirac $\delta$ distribution. Starting from the Bonnor rocket we explicitly construct the Schwarzschild solution witch conical singularity and the C-metric. In the latter case we show that there is a momentum flux through the cosmic string, causing the acceleration of the black hole and the amount of this momentum is in agreement with the momentum taken away by gravitational radiation.