2. Notations and definitions
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 , .
Any vector field satisfies the following identity
where is the Riemann curvature tensor (note that this identity may be regarded as defining the curvature tensor). The Ricci tensor is defined by
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 .
© European Southern Observatory (ESO) 1998
Online publication: October 22, 1998