Eur. Phys. J. Plus (2016) 131: 21
https://doi.org/10.1140/epjp/i2016-16021-y

Regular Article

Focusing of world-lines in Weyl gravity

Physics Department, Payame Noor University, 19395-3697, Tehran, Iran

^* e-mail: m-mohseni@pnu.ac.ir

Received: 15 December 2015
Accepted: 22 December 2015
Published online: 1 February 2016

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 coefficient 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.