Killing Vector Fields
The Lie algebra of Killing vector fields of a spherically symmetric static spacetime takes the same form in the isotropic chart as in the Schwarzschild chart. Namely, this algebra is generated by the timelike irrotational Killing vector field
and three spacelike Killing vector fields
Here, saying that is irrotational means that the vorticity tensor of the corresponding timelike congruence vanishes; thus, this Killing vector field is hypersurface orthogonal. The fact that the spacetime admits an irrotational timelike Killing vector field is in fact the defining characteristic of a static spacetime. One immediate consequence is that the constant time coordinate surfaces form a family of (isometric) spatial hyperslices (spacelike hypersurfaces).
Unlike the Schwarzschild chart, the isotropic chart is not well suited for constructing embedding diagrams of these hyperslices.
Read more about this topic: Isotropic Coordinates
Famous quotes containing the words killing and/or fields:
“Mrs. Finney: Cant we have some peace in this house, even on New Years Eve?
Sadie: You got it mixed up with Christmas. New Years Eve is when people go back to killing each other.”
—Joseph L. Mankiewicz (19091993)
“I was in love with a beautiful blonde once. She drove me to drink. Thats the one thing Im indebted to her for.”
—Otis Criblecoblis, U.S. screenwriter. W.C. Fields (W.C. Fields)