Dynamics of a self-gravitating thin string in scalar-tensor theories of gravitation

TL;DR

This paper investigates the behavior of a self-gravitating string within scalar-tensor gravity theories, revealing conditions under which the string's dynamics align with the Nambu-Goto model, including in massless dilatonic cases.

Contribution

It demonstrates that the extrinsic curvature of a thin string's world sheet generally vanishes in the zero-radius limit, and under specific constraints, the dynamics reduce to Nambu-Goto form.

Findings

Extrinsic curvature tends to zero as string radius shrinks.

Nambu-Goto dynamics emerge under certain solution constraints.

Analysis applies to massless dilatonic gravity theories.

Abstract

We examine the dynamics of a self-gravitating string in the scalar-tensor theories of gravitation by considering a thin tube of matter to describe it. For a class of solutions, we obtain in the generic case that the extrinsic curvature of the world sheet of the central line is null in the limit where the radius of the string tends to zero. However, if we impose a specific constraint on the behaviour of the solution then we find that only the mean curvature of the world sheet of the central line vanishes which is just the Nambu-Goto dynamics. This analysis can include the massless dilatonic theories of gravity.