Regularised Kalb-Ramond Magnetic Monopole with Finite Energy

TL;DR

This paper presents a regularized, finite-energy magnetic monopole solution inspired by string theory, involving Kalb-Ramond axions, with a calculable shell size and positive gravitational effects, contrasting with global monopoles.

Contribution

It introduces a method to determine the monopole's shell size by matching an inner de Sitter space with an outer Reissner-Nordström metric, ensuring positive gravitational mass.

Findings

The monopole exhibits normal attractive gravity due to KR axions.

The shell size is explicitly calculated via Israel junction conditions.

The total energy of the monopole is finite and proportional to the KR-axion charge.

Abstract

In a previous work we suggested a self-gravitating electromagnetic monopole solution in a string-inspired model involving global spontaneous breaking of a $SO(3)$ internal symmetry and Kalb-Ramond (KR) axions, stemming from an antisymmetric tensor field in the massless string multiplet. These axions carry a charge, which, in our model, also plays the r\^ole of the magnetic charge. The resulting geometry is close to that of a Reissner-Nordstr\"om (RN) black hole with charge proportional to the KR-axion charge. We proposed the existence of a thin shell structure inside a (large) core radius as the dominant mass contribution to the energy functional. The resulting energy was finite, and proportional to the KR-axion charge; however, the size of the shell was not determined and left as a phenomenological parameter. In the current article, we can calculate the mass-shell size, on proposing a regularisation of the black hole singularity via a matching procedure between the RN metric in the outer region and, in the inner region, a de Sitter space with a (positive) cosmological constant proportional to the scale of the spontaneous symmetry breaking of $SO(3)$ . The matching, which involves the Israel junction conditions for the metric and its first derivatives at the inner surface of the shell, determines the inner mass-shell radius. The axion charge plays an important r\^ole in guaranteeing positivity of the "mass coefficient" of the gravitational potential term appearing in the metric component; so the KR electromagnetic monopole shows normal attractive gravitational effects. This is to be contrasted with the global monopole case (in the absence of KR axions) where such a matching is known to yield a negative "mass coefficient" (and, hence, repulsive gravitational effects). The total energy of the monopole within the shell is calculated.