Exact solutions that describe boson or fermion stars have been found only numerically (in 3 + 1 dimensions). For this reason there is no boson star model for which the lightlike geodesics could be studied analytically. Numerical studies of lensing have been carried out by Dabrowski and Schunck  for a transparent spherically symmetric static maximal boson star, and by Bilić, Nikolić, and Viollier  for a transparent spherically symmetric static maximal fermion star. For the case of a fermion-fermion star (two components) see . In all three articles the authors use the “almost exact lens map” of Virbhadra and Ellis (see Section 4.3) which is valid for observer and light source in the asymptotic region and almost aligned. Dabrowski and Schunck  also discuss how the alignment assumption can be dropped. The lensing features found in  for the boson star and in  for the fermion star have several similarities. In both cases, there is a tangential caustic and a radial caustic (recall Figure 8 for terminology). A (point) source on the tangential caustic (i.e., on the axis of symmetry through the observer) is seen as a (1-dimenional) Einstein ring plus a (point) image in the center. If the (point) source is moved away from the axis the Einstein ring breaks into two (point) images, so there are three images altogether. Two of them merge and vanish if the radial caustic is crossed. So the qualitative lensing features are quite different from a Schwarzschild black hole with (theoretically) infinitely many images (see Section 5.1). The essential difference is that in the case of a boson or fermion star there are no circular lightlike geodesics towards which light rays could asymptotically spiral.
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