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Astron. Astrophys. 339, 921-928 (1998)

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2. Notations and definitions

The signature of the metric tensor [FORMULA] is assumed to be [FORMULA]. Indices are lowered with [FORMULA] and raised with [FORMULA].

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 [FORMULA]. Note that for any function [FORMULA], [FORMULA].

Any vector field [FORMULA] satisfies the following identity

[EQUATION]

where [FORMULA] is the Riemann curvature tensor (note that this identity may be regarded as defining the curvature tensor). The Ricci tensor is defined by

[EQUATION]

Given a quantity P, [FORMULA] 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 [FORMULA] is the Planck constant divided by [FORMULA].

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© European Southern Observatory (ESO) 1998

Online publication: October 22, 1998
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