The signature of the metric tensor is assumed to be (+ - - -). Indices are lowered with and raised with .
Greek letters run from 0 to 3. Latin letters are used for spatial coordinates only: they run from 1 to 3. A comma (,) denotes an ordinary partial differentiation. A semi-colon (;) denotes a covariant partial differentiation with respect to the metric; so . Note that for any function F(x), .
Any vector field satisfies the following identity
(1) |
(2) |
Given a quantity P, denotes its complex conjugate.
The subscripts em and obs in formulae stand respectively for emitter and observer.
The constant c is the speed of light and is the Planck constant divided by .