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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 Einsteinâ€™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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