  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 constraint 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 [Astrophys. J. 701, 1357 (2009); Astrophys. J. 805, 179 (2015)]. We find
that for rapidly spinning objects rotation can significantly affect the
escaping probability of 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 non-rotating 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*.
