Stationary BPS Solutions in N=2 Supergravity with R^2-Interactions

TL;DR

This work characterizes stationary BPS solutions in four-dimensional $N=2$ supergravity with $R^2$ interactions, using a holomorphic function $F(X,\hat{A})$ to capture higher-derivative terms. It shows that fully and partially supersymmetric configurations are governed by harmonic functions and generalized stabilization equations, with moduli fixed at the horizon by charges (fixed-point behavior) and duality-invariant structures shaping the solutions. The analysis extends known results to include $R^2$ corrections, derives the Wald entropy including $F_A$ contributions, and discusses implications for the near-horizon geometry and the moduli-space metric of extremal black holes. The framework lays groundwork for explicit multi-centered solutions and detailed moduli-space studies in the presence of higher-derivative interactions.

Abstract

We analyze a broad class of stationary solutions with residual N=1 supersymmetry of four-dimensional N=2 supergravity theories with terms quadratic in the Weyl tensor. These terms are encoded in a holomorphic function, which determines the most relevant part of the action and which plays a central role in our analysis. The solutions include extremal black holes and rotating field configurations, and may have multiple centers. We prove that they are expressed in terms of harmonic functions associated with the electric and magnetic charges carried by the solutions by a proper generalization of the so-called stabilization equations. Electric/magnetic duality is manifest throughout the analysis. We also prove that spacetimes with unbroken supersymmetry are fully determined by electric and magnetic charges. This result establishes the so-called fixed-point behavior according to which the moduli fields must flow towards certain prescribed values on a fully supersymmetric horizon, but now in a more general context with higher-order curvature interactions. We briefly comment on the implications of our results for the metric on the moduli space of extremal black hole solutions.