Work

Dyonic Kerr-Schild ansatz

Year: 2025

Type: article

Abstract: We develop a geometric extension of the Kerr-Schild ansatz that incorporates both electric and magnetic sectors of the Maxwell field in a unified framework, without resorting to duality rotations. We start observing that the known purely electric solution satisfies Maxwell’s equations due to a closedness condition obeyed by the Kerr-Schild null congruence. From the associated local exactness property, we construct a new 1-form naturally linked to the congruence as a sort of Poincaré dualization. This leads us to propose a geometrically motivated dyonic vector potential within the Kerr-Schild ansatz, defined as a superposition of an electric contribution along the congruence and a magnetic one that aligns to the dualized 1-form. We then show that for a stationary and axisymmetric Kerr-Schild ansatz, the electrovac circularity theorem uniquely constrains not only the scalar profile of the metric but also those associated with the electric-magnetic splitting of the gauge field. The resulting formalism provides a transparent derivation of the dyonic Kerr-Newman solution and extends naturally to the (A)dS case, highlighting the intrinsic interplay between geometry and matter in a Kerr-Schild setting.

Source: Physical review. D/Physical review. D.

DOI: 10.1103/l1f2-vxlc

Authors: Eloy Ayón-Beato, Daniel Flores-Alfonso, Mokhtar Hassaine, Daniel F. Higuita-Borja

Institutions: Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional, Universidad Autónoma Metropolitana, University of Talca, Universidad de Antioquia, Benemérita Universidad Autónoma de Puebla

Language: English

Topic: Black Holes and Theoretical Physics

Subfield: Nuclear and High Energy Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: hybrid

Funder: Consejo Nacional de Ciencia y Tecnología

Award: G5091783006