Quasi-topological Electromagnetism: Dark Energy, Dyonic Black Holes, Stable Photon Spheres and Hidden Electromagnetic Duality

TL;DR

This paper introduces quasi-topological electromagnetism, a model that can mimic dark energy and significantly alters dyonic black hole solutions, revealing new horizon structures, photon spheres, and electromagnetic duality properties.

Contribution

It presents the first study of quasi-topological electromagnetism's effects on black holes and cosmology, including modified dyonic solutions and a mechanism for dark energy coupling.

Findings

Dyonic black holes can have four horizons.

Black holes can host up to three photon spheres, including a stable one.

The model provides a dark energy mechanism and maintains duality in the on-shell action.

Abstract

We introduce the quasi-topological electromagnetism which is defined to be the squared norm of the topological 4-form $F\wedge F$. A salient property is that its energy-momentum tensor is of the isotropic perfect fluid with the pressure being precisely the opposite to its energy density. It can thus provide a model for dark energy. We study its application in both black hole physics and cosmology. The quasi-topological term has no effect on the purely electric or magnetic Reissner-Nordstr\"om black holes, the dyonic solution is however completely modified. We find that the dyonic black holes can have four real horizons. For suitable parameters, the black hole can admit as many as three photon spheres, with one being stable. Another intriguing property is that although the quasi-topological term breaks the electromagnetic duality, the symmetry emerges in the on-shell action in the Wheeler-DeWitt patch. In cosmology, we demonstrate that the quasi-topological term alone is equivalent to a cosmological constant, but the model provides a mechanism for the dark energy to couple with other types of matter. We present a concrete example of the quasi-topological electromagnetism coupled to a scalar field that admits the standard FLRW cosmological solutions.