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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. They can also be used to generate new solutions for Einstein equations by similarity reduction.[1]
See also
Affine vector field
Curvature collineation
Killing vector field
Matter collineation
Spacetime symmetries
References
Exact Solutions of Einstein’s Field Equations. Cambridge University Press. p. 163. ISBN 978-0-521-46136-8.
1 Exact solutions
2 Black hole uniqueness
3 See also
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