Shadows of rotating hairy Kerr black holes coupled to time periodic scalar fields with non-flat target space

Abstract: We study the shadows cast by rotating hairy black holes with two non-trivial time-periodic scalar fields having a non-flat Gaussian curvature of the target space spanned by the scalar fields. Such black holes are a viable alternative to the Kerr black hole, having a much more complicated geodesic structure and resulting shadows. We investigate how a nontrivial Gauss curvature alters the pictures for different amounts of scalar hair around the black holes, quantified by a normalized charge. Our results show that for high values of this charge, close to a boson star limit, chaotic shadows are observed with multiple small disconnected components for all considered Gaussian curvatures. For moderately large amounts of scalar hair and corresponding normalized charge, although the shadows still exhibit chaotic behavior, a dominant shadow component emerges, the size and shape of which are substantially influenced by the Gaussian curvature. For instance, highly chaotic shadows for flat target space, start developing a large central shadow region with the increase of the Gauss curvature even for black holes with substantially heavy scalar hair. For lower values of the normalized charge, the shadows resemble qualitatively the Kerr black hole while the Gaussian curvature has a small impact on their properties.