The Raychaudhuri equation for spinning test particles

TL;DR

This paper derives generalized Raychaudhuri equations for spinning test particles and analyzes their evolution in Kerr spacetime, providing insights into congruences of world-lines, momentum, and spin.

Contribution

It introduces new Raychaudhuri equations for spinning particles and compares their expansion parameters in Kerr spacetime, extending classical results.

Findings

Derived generalized Raychaudhuri equations for spinning particles.

Compared expansion evolution for different congruences in Kerr spacetime.

Provided physical interpretations for non-normalized, time-like, and space-like vectors.

Abstract

We obtain generalized Raychaudhuri equations for spinning test particles corresponding to congruences of particle's world-lines, momentum, and spin. These are physical examples of the Raychaudhuri equation for a non-normalized vector, unit time-like vector, and unit space-like vector. We compute and compare the evolution of expansion-like parameters associated with these congruences for spinning particles confined in the equatorial plane of the Kerr space-time.