Line Sources in Brans-Dicke Theory of Gravity

TL;DR

This paper explores the gravitational fields of line sources within Brans-Dicke gravity, extending methods from general relativity to include scalar fields and analyzing specific solutions and thin shell treatments.

Contribution

It adapts Israel's approach from general relativity to derive field equations for line sources in Brans-Dicke theory, incorporating scalar fields and examining particular solutions.

Findings

Derived field equations relating energy-momentum, scalar field, and extrinsic curvature.

Analyzed specific solutions including Gundlach and Ortiz.

Discussed methods for handling thin shells in Brans-Dicke gravity.

Abstract

We investigate how the gravitational field generated by line sources can be characterized in Brans-Dicke theory of gravity. Adapting an approach previously developed by Israel who solved the same problem in general relativity we show that in Brans-Dicke theory's case it is possible to work out the field equations which relate the energy-momentum tensor of the source to the scalar field, the coupling constant $\omega $ and the extrinsic curvature of a tube of constant geodesic radius centered on the line in the limit when the radius shrinks to zero. In this new scenario two examples are considered and an account of the Gundlach and Ortiz solution is included. Finally, a brief discussion of how to treat thin shells in Brans-Dicke theory is given.