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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.

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.

• Mathematical methods in general relativity