Geodesic Congruences and a Collapsing Stellar Distribution in f (T ) Theories

TL;DR

This paper investigates the dynamics of collapsing stellar bodies within f(T) gravity and nonminimally coupled scalar fields, using geodesic deviation to analyze congruences, revealing models that satisfy energy conditions and exhibit interesting collapse behaviors.

Contribution

It introduces a novel analysis of stellar collapse in f(T) gravity with scalar coupling, employing geodesic deviation instead of Raychaudhuri equation.

Findings

f(T) models satisfying null energy condition with specific collapse profiles

Potential scalar field-driven collapse models with unique evolution patterns

Identification of models with physically plausible collapse behaviors

Abstract

Teleparallel Gravity (TG) describes gravitation as a torsional- rather than curvature-based effect. As in curvature-based constructions of gravity, several different formulations can be proposed, one of which is the Teleparallel equivalent of General Relativity (TEGR) which is dynamically equivalent to GR. In this work, we explore the evolution of a spatially homogeneous collapsing stellar body in the context of two important modifications to TEGR, namely f (T) gravity which is the TG analogue of f (R) gravity, and a nonminimal coupling with a scalar field which has become popular in TG for its effects in cosmology. We explore the role of geodesic deviation to study the congruence of nearby particles in lieu of the Raychaudhuri equation. We find f (T) models that satisfy the null energy condition and describe interesting collapse profiles. In the case of a nonminimally coupled scalar field, we also find potential collapse models with intriguing scalar field evolution profiles.