Photon boomerang in a nearly extreme Kerr metric

Abstract

The Kerr rotating black hole metric has unstable photon orbits that orbit around the hole at fixed values of the Boyer-Lindquist coordinate r that depend on the axial angular momentum of the orbit, as well as on the parameters of the hole. For zero orbital axial angular momentum, these orbits cross the rotational axes at a fixed value of r that depends on the mass M and angular momentum J of the black hole. Nonzero angular momentum of the hole causes the photon orbit to rotate so that its direction when crossing the north polar axis changes from one crossing to the next by an angle I shall call ∆φ, which depends on the black hole dimensionless rotation parameter a/M = cJ/(GM2) by an equation involving a complete elliptic integral of the first kind. When the black hole has a/M ≈ 0.994 341 179 923 26, which is nearly maximally rotating, a photon sent out in a constant-r direction from the north polar axis at r ≈ 2.423 776 210 035 73 GM/c2returns to the north polar axis in precisely the opposite direction (in a frame nonrotating with respect to the distant stars), a photon boomerang.

Astrophysical consequences of dark matter for photon orbits and shadows of supermassive black holes

“…We intend to analyze the effect of the PFDM on the spherical photon orbits around BHs and NSs. We will extend the previous analysis in [17] to find the possible effects of surrounding PFDM on the boomerang orbits and also to inquire whether such orbits can be formed around NSs as well. Further, we will investigate how the PFDM affects the black hole shadow structure and compare our result with those of the Kerr BHs' [16].…”

“…left panel in Fig. 13) -termed photon boomerang [17]. In the Kerr case however, the phenomena of photon boomerang cannot occur in case of a NS, wherein, the requirement a > a E is not fulfilled for any r, on solving ∆φ = π.…”

“…Noteworthy attention is devoted to generalize the spherical photon orbits around Kerr BHs, for instance, to the case for Kerr naked singularities (NSs) [13], near-extremal Kerr BHs [14], deformed Kerr BH with an extra deformation parameter [15], and Myers-Perry BH [16]. Among the spherical photon orbits, an interesting case of photons returning to the same point in exactly opposite direction after one complete azimuthal oscillation -the photon boomerang-has been studied around the Kerr BH [17].…”