In spherical symmetry the “integrate null geodesics forwards” algorithm (Section 5.1) can be used, although the “integrate null geodesics backwards” and “integrate null surfaces backwards” algorithms (Sections 5.2 and 5.3 respectively) are more efficient.

In non-spherically-symmetric spacetimes the “integrate null surfaces backwards” algorithm (Section 5.3) is clearly the best algorithm known: It is efficient, accurate, and fairly easy to implement. For generic spacetimes, Diener’s event-horizon finder EHFinder [60] is particularly notable as a freely available implementation of this algorithm as a module (“thorn”) in the widely-used Cactus computational toolkit (see Table 2).

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