Linear Einstein equations and Kerr-Schild maps

Details Linear Einstein equations and Kerr-Schild maps Linear Einstein equations and Kerr-Schild maps

2002-03-28

arxiv.org/abs/gr-qc/0203101v1

Class.Quant.Grav. 19 (2002) 2515

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

9 pages, accepted by Class. Quant. Grav

Scientific paper

10.1088/0264-9381/19/9/313

We prove that given a solution of the Einstein equations $g_{ab}$ for the matter field $T_{ab}$, an autoparallel null vector field $l^{a}$ and a solution $(l_{a}l_{c}, \mathcal{T}_{ac})$ of the linearized Einstein equation on the given background, the Kerr-Schild metric $g_{ac}+\lambda l_{a}l_{c}$ ($\lambda $ arbitrary constant) is an exact solution of the Einstein equation for the energy-momentum tensor $T_{ac}+\lambda \mathcal{T}_{ac}+\lambda ^{2}l_{(a}\mathcal{T}_{c)b}l^{b}$. 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 space-time due to G\"{u}rses and G\"{u}rsey.

Affiliated with

Also associated with

No associations

Rating

Linear Einstein equations and Kerr-Schild maps does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Linear Einstein equations and Kerr-Schild maps, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Linear Einstein equations and Kerr-Schild maps will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-63788