Evolution of geodesic congruences in a gravitationally collapsing scalar field background

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.

Raychaudhuri equation in the Finsler–Randers space-time and generalized scalar-tensor theories

“…where A i (x) is the electromagnetic potential and g ij (x) the Riemannian gravitational potential with ẋi = dx i ds . From (19) we get…”

“…Raychaudhuri equation has been introduced by A.Raychaudhuri [1]. It is a fundamental equation in gravitation and cosmology and has been studied and generalized in many ways, in different cases [2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21]. In Finsler space-time this equation was introduced in [22], [23], [24] and later studied in a different way [25] .…”

A wormhole geometry from gravitational collapse

“…Evolution of such quantities along a geodesic congruence are governed by the Raychaudhuri equations [44]. Although the kinematic quantities for geodesic congruences are wellstudied for static spacetime geometries [45], a non-static collapsing spacetime has received less attention in this regard [46].…”

Γενικευμένες Θεωρίες Βαρύτητας Σε Κοσμολογικά Πρότυπα

“…Η εξίσωση Raychaudhuri έχει εισαχθεί από τον Raychaudhuri [137]. Είναι μια θεμελιώδης εξίσωση για τη βαρύτητα και την κοσμολογία και έχει μελετηθεί και γενικευθεί με πολλούς τρόπους σε διαφορετικές περιπτώσεις [58], [7], [64], [122], [126], [53], [92], [94] [80], [106], [54], [2], [123], [4], [140], [3], [142], [37], [93]. Αυτή η εξίσωση έχει εισαχθεί [162], [163], [171] και έχει μελετηθεί επίσης στο χωροχρόνο Finsler [118].…”