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

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