Exact electromagnetic duality with nonminimal couplings

Abstract

We study dyonic black hole solutions in the simplest nonminimal extension of Einstein-Maxwell theory that preserves electromagnetic duality. Any such theory involves an infinite tower of higherderivative terms whose computation and summation usually represents an inaccessible problem. However, we show that upon assumption of a static and spherically symmetric ansatz, the whole series of higher-curvature terms can be summed up, giving rise to a fully nonlinear reduced action whose equations of motion are invariant under rotations of the electric and magnetic charges. From this result we compute the perturbative corrections to the Reissner-Nordström solution, and in the case of extremal black holes we determine exactly the near-horizon geometry as well as the entropy. Remarkably, the entropy only possesses a constant correction despite the action containing an infinite number of terms. In addition, we find there is a lower bound for the charge and the mass of extremal black holes. When the sign of the coupling is such that the weak gravity conjecture is satisfied, the area and the entropy of extremal black holes vanish at the minimal charge.

Introductory Notes on Non‐linear Electrodynamics and its Applications

“…More explicit examples of duality-invariant NED Lagrangians were found in [51]. A generalization of this condition to the case of electrodynamics non-minimally coupled to a higher-curvature gravity was recently considered in [52,53].…”

“…For instance, NEDs coupled to gravity have been used to construct new black hole solutions and study their properties and stability (see e.g. [8-10, 12, 35, 77-95] and also [21,52,53,[96][97][98][99][100][101][102][103][104][105] for the latest developments and review), to create cosmological models (which might avoid initial Big-Bang singularities), [106,107] to mimic dark energy and generate an accelerated expansion of the universe, [108][109][110][111][112][113][114][115] as well as the context of AdS/CFT correspondence and gravity/CMT holography (see e.g. [14,[116][117][118][119][120][121][122] and [123] for a recent review and more references).…”