'Square Root' of the Maxwell Lagrangian versus confinement in general relativity

TL;DR

This paper investigates the use of the square root of the Maxwell Lagrangian coupled with gravity to find confining potentials, revealing that magnetic charges do not produce confinement but electric charges can in specific spacetimes.

Contribution

It demonstrates that confining potentials can exist with the square root Maxwell Lagrangian in Nariai-Bertotti-Robinson spacetimes even without the standard Maxwell term, contrasting previous findings.

Findings

No confining potential with magnetic charge in this model.

Confining potentials found for electric charges in NBR spacetimes.

Confinement persists even when the standard Maxwell Lagrangian is relaxed.

Abstract

We employ the 'square root' of the Maxwell Lagrangian (i.e. \surd(F_{{\mu}{\nu}}F^{{\mu}{\nu}})), coupled with gravity to search for the possible linear potentials which are believed to play role in confinement. It is found that in the presence of magnetic charge no confining potential exists in such a model. Confining field solutions are found for radial geodesics in pure electrically charged Nariai- Bertotti-Robinson (NBR)-type spacetime with constant scalar curvature. Recently, Guendelman, Kaganovich, Nissimov and Pacheva, [Phys.Lett.B704(2011)230] have shown that superposed square root with standard Maxwell Lagrangians yields confining potentials in spherically symmetric spacetimes with new generalized Reissner-Nordstr\"om-de Sitter / -anti-de Sitter black hole solutions. In NBR spacetimes we show that confining potentials exist even when the standard Maxwell Lagrangian is relaxed.