# Deadly Orbit Spacetime & Curvature Symmetries Lyrics

s___etime Symmetries:

s___etime symmetries refers to aspects of s___etime that can be described as exhibiting some form of symmetry. The role of symmetry in physics is important, for example, in simplifying solutions to many problems. s___etime symmetries are used to simplify problems and find ample application in the study of exact solutions of Einstein's field equations of general relativity.

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Curvature symmetry

A curvature collineation is a vector field which preserves the Riemann tensor:

where Rabcd are the components of the Riemann tensor. The set of all smooth curvature collineations forms a Lie algebra under the Lie bracket operation (if the smoothness condition is dropped, the set of all curvature collineations need not form a Lie algebra). The Lie algebra is denoted by CC(M) and may be infinite-dimensional. Every affine vector field is a curvature collineation.

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