## 2. Notations and definitionsThe 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 The subscripts The constant © European Southern Observatory (ESO) 1998 Online publication: October 22, 1998 |