Cosmic String and Black Hole Limits of Toroidal Vlasov Bodies in General Relativity

TL;DR

This paper numerically explores the limits of stationary, toroidal Einstein-Vlasov solutions with angular momentum, revealing connections to extremal Kerr black holes and cosmic string models in general relativity.

Contribution

It introduces a numerical analysis of relativistic toroidal Vlasov bodies, identifying their approach to Kerr black holes and cosmic string configurations.

Findings

Solutions approach extremal Kerr black holes as relativistic limit

High angular momentum solutions exhibit conical geometry with deficit angles

Potential models for rotating cosmic strings are proposed

Abstract

We numerically investigate limits of a two-parameter family of stationary solutions to the Einstein-Vlasov system. The solutions are toroidal and have non-vanishing angular momentum. As one tunes to more relativistic solutions (measured for example by an increasing redshift) there exists a sequence of solutions which approaches the extreme Kerr black hole family. Solutions with angular momentum larger than the square of the mass are also investigated, and in the relativistic limit the near-field geometry of such solutions is observed to become conical in the sense that there is a deficit angle. Such solutions may provide self-consistent models for rotating circular cosmic strings.