Abstract
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.
Highlights
We study higher-order corrections to two BPS solutions of 5D supergravity, namely the supersymmetric black ring and the spinning black hole
The section derives the R2 corrections to the 5D entropy as horizon integrals of curvature components using Wald’s formula
In the following we will evaluate this correction for the spinning black hole and black ring solutions
Summary
We will use Wald’s formula to derive an expression for R2 corrections to the 5D entropy. Modifications to the area law due to the additional terms in the action - these terms are evaluated using the zeroth order solutions for the metric and the other fields. Modification of the area due to the change of the metric on the horizon, which follows from the fact that adding extra terms to the action may change the equations of motion. In 4D, the second type of modification is absent at leading order for this particular R2 form of ∆I obtained by reduction of (1) [15]. This and the 4D-5D agreement we find to leading order suggest that this may be the case in 5D as well. In the following we will evaluate this correction for the spinning black hole and black ring solutions
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