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In general relativity, optical scalars refer to a set of three scalar functions { θ ^ {\displaystyle \{{\hat {\theta }}} , σ ^ {\displaystyle {\hat {\sigma }}} and ω ^ {\displaystyle {\hat {\omega }}} } {\displaystyle \}} describing the propagation of a geodesic null congruence.
In fact, these three scalars { θ ^ , σ ^ , ω ^ } {\displaystyle \{{\hat {\theta }}\,,{\hat {\sigma }}\,,{\hat {\omega }}\}} can be defined for both timelike and null geodesic congruences in an identical spirit, but they are called "optical scalars" only for the null case. Also, it is their tensorial predecessors { θ ^ h ^ a b , σ ^ a b , ω ^ a b } {\displaystyle \{{\hat {\theta }}{\hat {h}}_{ab}\,,{\hat {\sigma }}_{ab}\,,{\hat {\omega }}_{ab}\}} that are adopted in tensorial equations, while the scalars { θ ^ , σ ^ , ω ^ } {\displaystyle \{{\hat {\theta }}\,,{\hat {\sigma }}\,,{\hat {\omega }}\}} mainly show up in equations written in the language of Newman–Penrose formalism.
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