Relativistic Plasticity

Abstract

The elastic crust of a neutron star has long been established as a key player in relevant aspects of neutron star physics. However, the state-of-the-art theory of elasticity is restricted to the perturbative domain and does not account for permanent plastic deformations which should be relevant for pulsar glitches, magnetar flares, and the continuous emission of gravitational waves. Plasticity, however, is a historically challenging phenomenon to model - even in the Newtonian regime. This is owed mainly to its dissipative character and the multiscale methods required to consistently reproduce observed phenomena. In this work, we address this first challenge by making use of recent developments in the variational modelling of dissipative fluids to extend the theory of relativistic elasticity to include plastic phenomenology. The resulting theory possesses the same freedoms as the modern Newtonian formalism, while now being compatible with general relativity. The second law of thermodynamics is then used to introduce the yield criterion of plasticity theory in the relativistic setting.