Stationary Axion/Dilaton Solutions and Supersymmetry

TL;DR

This paper introduces a new class of supersymmetric stationary solutions in N=4 supergravity, generalizing known solutions and revealing duality-invariant properties, with implications for black hole and rotating spacetime geometries.

Contribution

It provides a novel set of duality-invariant, supersymmetric solutions characterized by harmonic functions and constants, extending previous solutions and analyzing their horizon and supersymmetry properties.

Findings

Solutions include rotating asymptotically Taub-NUT metrics.

Static solutions describe supersymmetric extremal black holes.

Stationary solutions with angular momentum are not black holes.

Abstract

We present a new set of supersymmetric stationary solutions of pure N=4,d=4 supergravity (and, hence, of low-energy effective string theory) that generalize (and include) the Israel-Wilson-Perj\'es solutions of Einstein-Maxwell theory. All solutions have 1/4 of the supersymmetries unbroken and some have 1/2. The full solution is determined by two arbitrary complex harmonic functions {\cal H}_{1,2} which transform as a doublet under SL(2,\R) S duality and N complex constants k^{(n)} that transform as an SO(N) vector. This set of solutions is, then, manifestly duality invariant. When the harmonic functions are chosen to have only one pole, all the general resulting point-like objects have supersymmetric rotating asymptotically Taub-NUT metrics with 1/2 or 1/4 of the supersymmetries unbroken. The static, asymptotically flat metrics describe supersymmetric extreme black holes. Only those breaking 3/4 of the supersymmetries have regular horizons. The stationary asymptotically flat metrics do not describe black holes when the angular momentum does not vanish, even in the case in which 3/4 of the supersymmetries are broken.