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

## TL;DR

This paper studies stationary supersymmetric solutions in N=2 supergravity with R^2 interactions, showing they are characterized by harmonic functions related to charges and establishing fixed-point behavior for moduli fields at horizons.

## Contribution

It generalizes the description of BPS solutions to include R^2 interactions, demonstrating their expression via harmonic functions and confirming fixed-point behavior in a broader context.

## Key findings

- Solutions are expressed in terms of harmonic functions linked to charges.
- Spacetimes with unbroken supersymmetry are fully determined by electric and magnetic charges.
- The fixed-point behavior of moduli fields extends to theories with higher-order curvature terms.

## 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.