Homothetic vector field

{{Short description|Vector field}}

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

:$\backslash mathcal\{L\}\_X\; g\_\{ab\}=2c\; g\_\{ab\}$

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.{{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]}}