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We show with the help of Fermat's principle that every lightlike geodesic inthe NUT metric projects to a geodesic of a two-dimensional Riemannian metricwhich we call the optical metric. The optical metric is defined on a(coordinate) cone whose opening angle is determined by the impact parameter ofthe lightlike geodesic. We show that, surprisingly, the optical metrics oncones with different opening angles are locally (but not globally) isometric.With the help of the Gauss-Bonnet theorem we demonstrate that the deflectionangle of a lightlike geodesic is determined by an area integral over theGaussian curvature of the optical metric. A similar result is known to be truefor static and spherically symmetric spacetimes. The generalisation to the NUTspacetime, which is neither static nor spherically symmetric (at least not inthe usual sense), is rather non-trivial.

Application of the Gauss-Bonnet theorem to lensing in the NUT metric