# Non-Riemmanian geometry, force-free magnetospheres and the generalized Grad-Shafranov equation

## TL;DR

This paper extends the Grad-Shafranov equation within a non-Riemannian gravity framework with torsion to model magnetar magnetospheres, revealing modifications in electrodynamic parameters while maintaining pair production rates.

## Contribution

It introduces a generalized Grad-Shafranov equation in a non-Riemannian geometry, incorporating torsion effects into magnetosphere modeling, a novel approach beyond standard GR.

## Key findings

- Modified electrodynamic parameters in the generalized framework
- The pair production rate remains unchanged
- Potential implications for gravitational wave energy emission

## Abstract

The magnetosphere structure of a magnetar is considered in the context of a theory of gravity with dynamical torsion field beyond the standard General Relativity (GR). To this end, the axially symmetric version of the Grad-Shafranov equation (GSE) is obtained in this theoretical framework. The resulting GSE solution in the case of the magnetosphere corresponds to a stream function containing also a pseudoscalar part. This function solution under axisymmetry presents a complex character that (as in the quantum field theoretical case) could be associated with an axidilaton field. Magnetar-pulsar mechanism is suggested and the conjecture about the origin of the excess energy due the GSE describing the magnetosphere dynamics is claimed. We also show that two main parameters of the electrodynamic processes (as described in GR framework by Goldreich and Julian (GJ) in 1969 [5]) are modified but the electron-positron pair rate N remains invariant. The possible application of our generalized equation (defined in a non-Riemannian geometry) to astrophysical scenarios involving emission of energy by gravitational waves, as described in the context of GR in [18], is briefly discussed.