Exact multiblack hole spacetimes in Einstein-ModMax theory

TL;DR

This paper presents exact multi-black hole solutions in Einstein-ModMax theory, a nonlinear electrodynamics model with duality and conformal invariance, revealing regular extremal solutions and generalizations including magnetic and dyonic charges, with cosmological constant extensions.

Contribution

The paper provides the first exact multi-black hole solutions in Einstein-ModMax nonlinear electrodynamics, including extremal, magnetic, dyonic, and cosmological constant cases.

Findings

Extremal solutions are regular outside the horizon.

Nonextremal solutions have conical singularities.

Solutions include magnetic, dyonic, and cosmological constant extensions.

Abstract

Exact solutions describing multiple, electrically charged black holes (BHs) in a model of nonlinear electrodynamics (NLE) minimally coupled to Einstein's gravity are presented. The NLE model is ModMax theory, that has attracted much attention due to its duality and conformal invariance, features shared with standard (linear) electrodynamics. In the nonextremal case, the solution has conical singularities, similarly to the multi Reissner-Nordstr\"om solution in Einstein-Maxwell theory. In the extremal case the solution is regular on and outside the event horizon; it is isometric to the Majumdar-Papapetrou solution, although the individual BHs have a nonunitary charge to mass ratio, due to screening effects. Using the ModMax electromagnetic duality invariance, magnetically charged and dyonic generalizations are also obtained. Finally, we construct multi-BH solutions with a positive cosmological constant.