Focusing of world-lines in Weyl gravity

TL;DR

This paper investigates how time-like world-lines focus in Weyl gravity, analyzing the convergence behavior of congruences through the Raychaudhuri equation and effects of conformal transformations.

Contribution

It provides a detailed analysis of world-line focusing in Weyl gravity, including effects of parameters and conformal transformations, which was not extensively studied before.

Findings

Positive linear coefficient leads to convergence of incoming rays

Negative coefficient results in different congruence behaviors

Conformal transformations affect the evolution of world-line congruences

Abstract

We study the evolution of time-like congruences in the vacuum solutions of Weyl conformal theory of gravity. Using the Raycaudhuri equation, we show that for positive values of the coeffcient of the linear term in the solution and in the absence of the cosmological constant, the incoming rays converge. The evolution of the congruence for negative values is investigated for different values of the parameters. The behavior of the congruence under conformal transformations is also studied.