Homothetic vector field

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

${\displaystyle {\mathcal {L}}_{X}g_{ab}=2cg_{ab}}$

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
• Conformal Killing vector field
• Curvature collineation
• Killing vector field
• Matter collineation
• Spacetime symmetries

References

1. Exact Solutions of Einstein’s Field Equations. Cambridge University Press. 2003. pp. 163. ISBN 978-0-521-46136-8.