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<div>A '''homothetic vector field''' (sometimes '''homothetic collineation''' or '''homothety''') is a [[projective vector field]] which satisfies the condition:<br />
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:<math>\mathcal{L}_X g_{ab}=2c g_{ab}</math> <br />
<br />
where c is a real constant. Homothetic vector fields find application in the study of [[gravitational singularity|singularities]] in general relativity, also it can be used to generate new solutions for Einstein equations by similarity reduction.<ref>{{cite book|title=Exact Solutions of Einstein’s Field Equations|publisher=Cambridge University Press|isbn=978-0-521-46136-8|pages=163}}</ref> <br />
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==See also==<br />
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* [[Affine vector field]]<br />
* [[Curvature collineation]]<br />
* [[Killing vector field]]<br />
* [[Matter collineation]]<br />
* [[Spacetime symmetries]]<br />
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==References==<br />
{{Reflist}}<br />
<br />
{{relativity-stub}}<br />
[[Category:Mathematical methods in general relativity]]</div>87.167.229.70