Asymmetric dyonic multi-centered rotating black holes

TL;DR

The paper constructs exact multi-centered rotating black holes in 4D Einstein–Maxwell–dilaton theory by dimensional reduction from 5D vacuum gravity, extending Teo–Wan's equal-charge solutions to configurations with unequal electric and magnetic charges. Using a 3D gravity coupled to an $SL(3,\mathbb{R})$ nonlinear sigma model (Clément’s framework) and two harmonic functions, the authors generate multi-centered dyonic solutions parameterized by a global angle $\alpha$ that fixes the charge ratio at each center. They demonstrate regularity (no curvature singularities outside horizons), absence of conical defects and Dirac–Misner strings, and no closed timelike curves for aligned or anti-aligned spins, with horizons remaining extremal and their angular velocity vanishing. The solutions interpolate between known limits, including the Teo–Wan case at $\alpha=\pi/4$ and the static Majumdar–Papapetrou solution when $J_i=0$, and offer a framework for extending to more general theories with symmetric cosets, such as certain supergravity models.

Abstract

We construct an exact solution in four-dimensional Einstein-Maxwell-dilaton theory, describing multi-centered rotating black holes carrying both electric and magnetic charges, obtained via dimensional reduction from five-dimensional Einstein gravity. This generalizes the Majumdar-Papapetrou solution to the rotating case, and extends the recent multi-centered rotating black hole solutions of Teo and Wan to configurations with unequal electric and magnetic charges. The resulting spacetimes are free of curvature singularities, conical defects, Dirac-Misner strings, and closed timelike curves, both on and outside the horizons, provided that the black holes have either aligned or anti-aligned spin orientations.