Raychaudhuri equation in scalar-tensor theory

TL;DR

This paper explores how the Raychaudhuri equation affects geodesic focusing in scalar-tensor gravity theories, showing that under certain conditions, singularities can potentially be avoided.

Contribution

It analyzes the Raychaudhuri equation within scalar-tensor theories like Brans-Dicke and Bekenstein's, revealing conditions that may prevent singularity formation.

Findings

Violation of convergence condition possible

Singularity avoidance under certain assumptions

Application to static and cosmological models

Abstract

Implications of the Raychaudhuri equation in focusing of geodesic congruences are studied in the framework of scalar--tensor theory of gravity. Specifically, we investigate the Brans--Dicke theory and Bekenstein's scalar field theory. In both of these theories, we deal with a static spherically symmetric distribution and a spatially homogeneous and isotropic cosmological model as specific examples. We find that it is possible to violate the convergence condition under reasonable physical assumptions. This leads to the possibility of avoiding a singularity.