Evolution of geodesic congruences in a gravitationally collapsing scalar field background

TL;DR

This paper investigates how geodesic congruences evolve in a dynamic, inhomogeneous spacetime during scalar field gravitational collapse, revealing nonmonotonic expansion behavior influenced by initial conditions and spacetime parameters.

Contribution

It provides a detailed analysis of geodesic behavior in a collapsing scalar field background, highlighting the impact of initial conditions and metric parameters on focusing and expansion.

Findings

Expansion scalar can jump from negative to positive before focusing.

Nonmonotonic expansion behavior explained through expansion equation analysis.

Spacetime inhomogeneity and nonstaticity significantly affect geodesic evolution.

Abstract

The evolution of timelike geodesic congruences in a spherically symmetric, nonstatic, inhomogeneous spacetime representing gravitational collapse of a massless scalar field is studied. We delineate how initial values of the expansion, rotation and shear of a congruence, as well as the spacetime curvature, influence the global behavior and focusing properties of a family of trajectories. Under specific conditions, the expansion scalar is shown to exhibit a finite jump (from negative to positive value) before focusing eventually occurs. This nonmonotonic behavior of the expansion, observed in our numerical work, is successfully explained through an analysis of the equation for the expansion. Finally, we bring out the role of the metric parameters (related to nonstaticity and spatial inhomogeneity), in shaping the overall behavior of geodesic congruences.