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Homothetic vector field

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Title: Homothetic vector field  
Author: World Heritage Encyclopedia
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Subject: Killing vector field, Projective vector field, Affine vector field, Curvature collineation
Publisher: World Heritage Encyclopedia

Homothetic vector field

A homothetic vector field (sometimes homothetic collineation or homothety) is a projective vector field which satisfies the condition:

\mathcal{L}_X g_{ab}=2c g_{ab}

where c is a real constant. Homothetic vector fields find application in the study of singularities in general relativity, also it can be used to generate new solutions for Einstein equations by similarity reduction.[1]

See also


  1. ^ Exact Solutions of Einstein’s Field Equations. Cambridge University Press. p. 163. ISBN . 
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