{{Short description|Vector field}} In [[physics]], a '''homothetic vector field''' (sometimes '''homothetic collineation''' or '''homothety''') is a [[projective vector field]] which satisfies the condition:
:<math>\mathcal{L}_X g_{ab}=2c g_{ab}</math>
where c is a real constant. Homothetic vector fields find application in the study of [[gravitational singularity|singularities]] in [[general relativity]]. They can also be used to generate new solutions for Einstein equations by similarity reduction.<ref>{{cite book|title=Exact Solutions of Einstein's Field Equations|year=2003|url=https://archive.org/details/exactsolutionsei00step|url-access=limited|publisher=[[Cambridge University Press]]|isbn=978-0-521-46136-8|pages=[https://archive.org/details/exactsolutionsei00step/page/n194 163]}}</ref>
==See also==
* [[Affine vector field]] * [[Conformal Killing vector field]] * [[Curvature collineation]] * [[Killing vector field]] * [[Matter collineation]] * [[Spacetime symmetries]]
==References== {{Reflist}}
[[Category:Mathematics of general relativity]]
{{relativity-stub}} {{math-physics-stub}}