Some generalizations of the Raychaudhuri equation

Gabriel Abreu and Matt Visser
Phys. Rev. D 83, 104016 – Published 5 May 2011

Abstract

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.

  • Received 23 December 2010

DOI:https://doi.org/10.1103/PhysRevD.83.104016

© 2011 American Physical Society

Authors & Affiliations

Gabriel Abreu* and Matt Visser

  • School of Mathematics, Statistics, and Operations Research, Victoria University of Wellington, Wellington, New Zealand

  • *gabriel.abreu@msor.vuw.ac.nz
  • matt.visser@msor.vuw.ac.nz

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 83, Iss. 10 — 15 May 2011

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review D

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×