Linear Einstein equations and Kerr-Schild maps

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

We prove that given a solution of the Einstein equations gab for the matter field Tab, an autoparallel null vector field l a and a solution (lalc, Tac) of the linearized Einstein equation on the given background, the Kerr-Schild metric gac + λlalc (λ arbitrary constant) is an exact solution of the Einstein equation for the energy-momentum tensor Tac + λTac + λ2l( aTc)blb The mixed form of the Einstein equation for Kerr-Schild metrics with autoparallel null congruence is also linear. Some more technical conditions hold when the null congruence is not autoparallel. These results generalize previous theorems for vacuum due to Xanthopoulos and for flat seed spacetime due to Gürses and Gürsey.

Original languageEnglish
Pages (from-to)2515-2523
Number of pages9
JournalClassical and Quantum Gravity
Volume19
Issue number9
DOIs
Publication statusPublished - May 7 2002

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Einstein equations
congruences
seeds
theorems
kinetic energy
tensors
vacuum

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Linear Einstein equations and Kerr-Schild maps. / Gergely, L.

In: Classical and Quantum Gravity, Vol. 19, No. 9, 07.05.2002, p. 2515-2523.

Research output: Contribution to journalArticle

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