We consider the following question: may two different black holes (BHs) cast exactly the same shadow? In spherical symmetry, we show the necessary and sufficient condition for a static BH to be shadowdegenerate with Schwarzschild is that the dominant photonsphere of both has the same impact parameter, when corrected for the (potentially) different redshift of comparable observers in the different spacetimes. Such shadow-degenerate geometries are classified into two classes. The first shadowequivalent class contains metrics whose constant (areal) radius hypersurfaces are isometric to those of the Schwarzschild geometry, which is illustrated by the Simpson and Visser (SV) metric. The second shadow-degenerate class contains spacetimes with different redshift profiles and an explicit family of metrics within this class is presented. In the stationary, axi-symmetric case, we determine a sufficient condition for the metric to be shadow degenerate with Kerr for far-away observers. Again we provide two classes of examples. The first class contains metrics whose constant (Boyer-Lindquist-like) radius hypersurfaces are isometric to those of the Kerr geometry, which is illustrated by a rotating generalization of the SV metric, obtained by a modified Newman-Janis algorithm. The second class of examples pertains BHs that fail to have the standard north-south Z 2 symmetry, but nonetheless remain shadow degenerate with Kerr. The latter provides a sharp illustration that the shadow is not a probe of the horizon geometry. These examples illustrate that nonisometric BH spacetimes can cast the same shadow, albeit the lensing is generically different.

We investigate the null geodesic flow and in particular the light rings (LRs), fundamental photon orbits (FPOs) and shadows of a black hole (BH) immersed in a strong, uniform magnetic field, described by the Schwarzschilld-Melvin electrovacuum solution. The empty Melvin magnetic Universe contains a tube of planar LRs. Including a BH, for weak magnetic fields, the shadow becomes oblate, whereas the intrinsic horizon geometry becomes prolate. For strong magnetic fields (overcritical solutions), there are no LRs outside the BH horizon, a result explained using topological arguments. This feature, together with the light confining structure of the Melvin universe yields panoramic shadows, seen (almost) all around the equator of the observer's sky. Despite the lack of LRs, there are FPOs, including polar planar ones, which define the shadow edge. We also observe and discuss chaotic lensing, including in the empty Melvin universe, and multiple disconnected shadows.

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Obtaining solutions of the Einstein field equations describing spinning compact bodies is typically challenging. The Newman–Janis algorithm provides a procedure to obtain rotating spacetimes from a static, spherically symmetric, seed metric. It is not guaranteed, however, that the resulting rotating spacetime solves the same field equations as the seed. Moreover, the former may not be circular, and thus expressible in Boyer–Lindquist-like coordinates. Amongst the variations of the original procedure, a modified Newman–Janis algorithm (MNJA) has been proposed that, by construction, originates a circular, spinning spacetime, expressible in Boyer–Lindquist-like coordinates. As a down side, the procedure introduces an ambiguity, that requires extra assumptions on the matter content of the model. In this paper we observe that the rotating spacetimes obtained through the MNJA always admit separability of the Hamilton–Jacobi equation for the case of null geodesics, in which case, moreover, the aforementioned ambiguity has no impact, since it amounts to an overall metric conformal factor. We also show that the Hamilton–Jacobi equation for light rays propagating in a plasma admits separability if the plasma frequency obeys a certain constraint. As an illustration, we compute the shadow and lensing of some spinning black holes obtained by the MNJA.

Tidal forces are an important feature of General Relativity, which are related to the curvature tensor. We analyze the tidal tensor in Kerr spacetime, with emphasis on the case along the symmetry axis of the Kerr black hole, noting that tidal forces may vanish at a certain point, unlike in the Schwarzschild spacetime, using Boyer-Lindquist coordinates. We study in detail the effects of vanishing tidal forces in a body constituted of dust infalling along the symmetry axis. We find the geodesic deviation equations and solve them, numerically and analytically, for motion along the symmetry axis of the Kerr geometry. We also point out that the intrinsic Gaussian curvature of the event horizon at the symmetry axis is equal to the component along this axis of the tidal tensor there.