How to describe the Sweet-Parker model in general relativity

TL;DR

This paper explores how the classical Sweet-Parker model of magnetic reconnection can be extended to general relativity, concluding that spacetime curvature does not alter the model's properties but observational frames can cause differences.

Contribution

It provides a relativistic reformulation of the Sweet-Parker model and clarifies the effects of spacetime curvature and observation frame on magnetic reconnection.

Findings

Spacetime curvature does not modify the Sweet-Parker model properties.

Observation frame affects the measured reconnection rate and outflow speed.

Relativistic effects are significant in astrophysical magnetic reconnection scenarios.

Abstract

It is a hot topic nowadays that magnetic reconnection, as a physical process to release magnetic energy effectively, occurs in numerous complicated astrophysical systems. Since the magnetic reconnection is thought to occur frequently in the accretion flow around compact objects which induce strong gravitational field, it is now regarded to be a practical mechanism to extract energy from rotation black holes, which motivates people to consider how to describe the process of magnetic reconnection in a generally relativistic way. In this work, I try to explore the description of Sweet-Parker model, one of the most famous theoretical models of magnetic reconnection, in general relativity. I begin with revisiting the Sweet-Parker model in special relativity and reorganize the calculations in seven steps, whose generally relativistic forms are discussed. I propose in this work, from the general discussions and consequences of specific examples, that no property in Sweet-Parker model would be modified by spacetime curvature, which is opposite to the conclusions in previous work. However, on the contrary, observation in different rest frames may bring modifications. If the magnetic reconnection occurs not in the rest frame of observer, the observer would find out that the detected relation between the reconnection rate and Lundquist number or that between outflow speed and Alfven velocity are not the same as the detected relations if the magnetic reconnection occurs just in the rest frame of observer.