Law of elasticity and fracture limit of magnetic forcelines under their gravitational deformation

TL;DR

This paper explores the elastic properties and fracture limits of magnetic fields in astrophysical objects, revealing how they resist gravitational deformation and ultimately succumb, with applications to neutron stars and white dwarfs.

Contribution

It introduces a law of elasticity for magnetic fields under gravitational deformation and calculates their fracture limits, linking magnetic elasticity with general relativity.

Findings

Magnetic fields exhibit elastic behavior under gravitational stress.

Magnetic fracture limits are quantified in astrophysical contexts.

Magnetic fields ultimately fail against gravitational contraction.

Abstract

Magnetic fields are a very special form of elastic medium. Within astrophysical environments (magnetised stars and protogalaxies) they counteract shear and rotational distortions as well as gravitational collapse. Their vector nature allows for their extraordinary coupling with spacetime curvature in the framework of general relativity. This particular coupling points out the way to study magnetic elasticity under gravitational deformation. In this context, we reveal their law of elasticity, calculate their fracture limit and subsequently argue that they ultimately lose the battle against gravitational contraction of magnetised matter. Two illustrative applications, in a neutron star and a white dwarf, accompany the results.