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

References

  1. ↑ Exact Solutions of Einstein’s Field Equations. Cambridge University Press. p. 163. ISBN 978-0-521-46136-8.