Shadow of a disformal Kerr black hole in quadratic degenerate higher-order scalar–tensor theories

We have studied the shadow of a disformal Kerr black hole with an extra deformation parameter, which belongs to non-stealth rotating solutions in quadratic degenerate higher-order scalar–tensor (DHOST) theory. Our result show that the size of the shadow increases with the deformation parameter for the black hole with arbitrary spin parameter. However, the effect of the deformation parameter on the shadow shape depends heavily on the spin parameter of black hole and the sign of the deformation parameter. The change of the shadow shape becomes more distinct for the black hole with the more quickly rotation and the more negative deformation parameter. Especially, for the near-extreme black hole with negative deformation parameter, there exist a “pedicel”-like structure appeared in the shadow, which increases with the absolute value of deformation parameter. The eyebrow-like shadow and the self-similar fractal structures also appear in the shadow for the disformal Kerr black hole in DHOST theory. These features in the black hole shadow originating from the scalar field could help us to understand the non-stealth disformal Kerr black hole and quadratic DHOST theory.