  We study higher-order corrections to two BPS solutions of 5D supergravity,
namely the supersymmetric black ring and the spinning black hole. Due in part
to our current relatively limited understanding of F-type terms in 5D
supergravity, the nature of these corrections is less clear than that of their
4D cousins. Effects of certain $R^2$ terms found in Calabi-Yau compactification
of M-theory are specifically considered. For the case of the black ring, for
which the microscopic origin of the entropy is generally known, the
corresponding higher order macroscopic correction to the entropy is found to
match a microscopic correction, while for the spinning black hole the
corrections are partially matched to those of a 4D $D0-D2-D6$ black hole.

High Energy Physics - Theory