The interest in the implications that astrophysical observations have for the understanding of the structure of black holes has grown since the first detection of gravitational waves. Many arguments that are put forward in order to constrain alternative black hole models rely on substantial assumptions such as perfect spherical symmetry, which implies absence of rotation. However, given that astrophysical black holes will generally exhibit nonzero angular momentum, realistic constraints must take into account the effects of rotation. In this work we analyze the gravitational effect that rotation has on the emission from the surface of ultracompact objects, by studying how angular momentum affects the propagation of light rays. This allows us to evaluate the reliability of the constraints derived for supermassive black holes (more specifically, Sagittarius A∗ and M87∗) assuming lack of rotation [as presented in A. E. Broderick, A. Loeb, and R. Narayan, Astrophys. J. 701, 1357 (2009)ASJOAB0004-637X10.1088/0004-637X/701/2/1357; A. E. Broderick et al. Astrophys. J. 805, 179 (2015)ASJOAB0004-637X10.1088/0004-637X/805/2/179]. We find that for rapidly spinning objects rotation can significantly affect the escaping probability of a photon emitted from the surface of the object, with a significant increase at the equatorial regions and a decrease at the poles with respect to the nonrotating case. For not so rapidly spinning black hole candidates like Sagittarius A∗, such modifications do not affect significantly the present constraints, which are nevertheless weaker than originally supposed due to the relativistic lensing here considered and additional phenomenological parameters that describe basic processes such as absorption. However, taking into account the angular dependence of the superficial emission of rapidly spinning black hole mimickers will be necessary for future studies of objects like e.g., M87∗.
