Conic Sections on the Sky: Shadows of Linearly Superrotated Black Holes

Soft hairs are an intrinsic infrared feature of a black hole, which may also affect near-horizon physics. In this work, we study some of the subtleties surrounding one of the primary observables with which we can study their effects in the context of Einstein's gravity: the black hole shadow. First, we clarify the singular pathology associated with black holes with soft hairs and demonstrate the metrics of linearly superrotated black holes are free of near-zone pathologies due to appropriate asymptotic falloff conditions imposed on the event horizon. We then analytically construct the photon orbits around such black holes and derive the shadow equation, and find that the linear superrotation hairs will deform the circular shadow of a bald Schwarzchild black hole into ellipses. This is in sharp contrast to their supertranslated counterparts, which only shift the position of the center of the circular shadow but do not change its shape. Our results suggest a richness to the observable effects due to the infrared structures of Einstein's gravity and demand their observations by future black hole imaging projects.
Comment: 10 pages, 2 figures, v2. Clarify the near-horizon pathology and reinterpret the regular metric we consider as the one with the near-horizon superrotation hairs. The main result of the shadow deformation does not change