Spinning extremal dyonic black holes in $γ=1$ Einstein-Maxwell-dilaton theory

TL;DR

This work tackles the existence and structure of spinning, dyonic extremal black holes in four-dimensional Einstein-Maxwell-dilaton theory at the stringy coupling $\gamma=1$. By combining a general numerical framework for the full bulk equations with an analytic near-horizon (NH) decoupling analysis, the authors reveal that regular solutions require equal electric and magnetic charges $P=Q$, and they map out a one-parameter family of regular eBHs that connect to Kerr but terminate at a critical angular momentum. The NH study yields a tractable set of ordinary differential equations for the NH data and first integrals that explain the regularity constraint, while perturbative and slowly rotating analyses further corroborate the special role of $P=Q$ and reveal how the NH data constrain bulk charges and horizon area. Nonperturbative numerics confirm the existence of these regular eBHs, show that bulk solutions cease to exist beyond a critical $j$, and demonstrate consistency between NH and bulk quantities. Overall, the paper provides a comprehensive framework and concrete results for regular spinning dyonic extremal black holes in EMd theory at $\gamma=1$, with implications for NH holography and (non)supersymmetric extremal black hole physics.

Abstract

We propose a general framework for the study of asymptotically flat spinning dyonic {\it extremal} black holes (eBHs) in $D=4$ Einstein-Maxwell-dilaton theory. Restricting to the stringy value $γ=1$ of the dilaton coupling constant, we report on the existence of a one parameter family of eBHs which are free of pathologies, provided their magnetic and electric charges are equal. An understanding of this condition is found from a study of the near horizon limit of the solutions, both perturbative closed form and numerical solutions being presented.

Figures (3)

• Figure 1: Left: The electric charge and the event horizon area (inset) are shown as a function of angular momentum for $\gamma=1$ extremal BH solutions (all quantities are given in units of mass). Right: The ratio between horizon angular momentum and total angular momentum together with the value of the scalar field at $\theta=0$ on the horizon are shown as a function of angular momentum.
• Figure 2: Left: The Ricci and Kretschmann scalars (in units of mass) are shown for a typical $\gamma=1$ dyonic spinning BH with $j=0.825$. Right: The energy density as measured by a unit energy particle infalling along a radial geodesic at $\theta=\pi/2$ is shown for the same solution, together with the scalar field profile at three different angles.
• Figure 3: Left: The profile of a typical rotating near horizon solution with $\gamma=1$. Right: A comparison between the results for extremal (smooth) BH solutions (red curve) and near horizon configurations (blue dotted curve). The two curves coincide up to the critical configuration $C$, only.