Axisymmetric Gravitational Solutions as Possible Classical Backgrounds around Closed String Mass Distributions

TL;DR

This paper investigates axisymmetric solutions in general relativity, suggesting they can represent classical backgrounds around closed string-like mass distributions by analyzing singularities and their regularizations.

Contribution

It demonstrates that certain axisymmetric solutions can be interpreted as classical backgrounds around closed strings, supported by regulator-independent singularity analysis.

Findings

Singularities in Kerr and Tomimatsu-Sato solutions resemble closed string mass distributions.

Regularization methods confirm the string-like nature of these singularities.

These solutions may serve as classical backgrounds for closed strings in general relativity.

Abstract

By studying singularities in stationary axisymmetric Kerr and Tomimatsu-Sato solutions with distortion parameter \d = 2, 3, ... in general relativity, we conclude that these singularities can be regarded as nothing other than closed string-like circular mass distributions. We use two different regularizations to identify \d-function type singularities in the energy-momentum tensor for these solutions, realizing a regulator independent result. This result gives supporting evidence that these axisymmetric exact solutions may well be the classical solutions around closed string-like mass distributions, just like Schwarzschild solution corresponding to a point mass distribution. In other words, these axisymmetric exact solutions may well provide the classical backgrounds around closed strings.