Some generalizations of the Raychaudhuri equation

Journal Article · Sun May 15 04:00:00 EDT 2011 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.83.104016· OSTI ID:21502587

Abreu, Gabriel; Visser, Matt ^[1]

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1. School of Mathematics, Statistics, and Operations Research, Victoria University of Wellington, Wellington (New Zealand)

The Raychaudhuri equation has seen extensive use in general relativity, most notably in the development of various singularity theorems. In this rather technical article we shall generalize the Raychaudhuri equation in several ways. First an improved version of the standard timelike Raychaudhuri equation is developed, where several key terms are lumped together as a divergence. This already has a number of interesting applications, both within the Arnowitt-Deser-Misner formalism and elsewhere. Second, a spacelike version of the Raychaudhuri equation is briefly discussed. Third, a version of the Raychaudhuri equation is developed that does not depend on the use of normalized congruences. This leads to useful formulae for the 'diagonal' part of the Ricci tensor. Fourth, a 'two vector' version of the Raychaudhuri equation is developed that uses two congruences to effectively extract 'off-diagonal' information concerning the Ricci tensor.

• OSTI ID: 21502587
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 10 Vol. 83; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
EQUATIONS
FIELD THEORIES
GENERAL RELATIVITY THEORY
RELATIVITY THEORY
RICCI TENSOR
SIMULATION
SINGULARITY
TENSORS