Frederic H. Vincent, Eric Gourgoulhon, Jérôme Novak
The equations governing null and timelike geodesics are derived within the 3+1 formalism of general relativity. In addition to the particle's position, they encompass an evolution equation for the particle's energy leading to a 3+1 expression of the redshift factor for photons. An important application is the computation of images and spectra in spacetimes arising from numerical relativity, via the ray-tracing technique. This is illustrated here by images of numerically computed stationary neutron stars and dynamical neutron stars collapsing to a black hole.
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http://arxiv.org/abs/1208.3927
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