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}=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]

References

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

This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.

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

Homothetic vector field

See also

References