Dissipation and turbulence in general relativistic hydrodynamics

TL;DR

This paper advances multi-fluid models in General Relativity, focusing on dissipative fluids and turbulence, with applications to neutron star mergers, proposing novel filtering schemes and analyzing key physical processes.

Contribution

It introduces a new model for dissipative multi-fluids in General Relativity and a consistent filtering scheme for turbulence in curved spacetime, with applications to neutron star phenomena.

Findings

Proposed a novel filtering scheme compatible with General Relativity.

Analyzed reactions as dominant dissipative sources in neutron star mergers.

Discussed magneto-rotational instability's role in turbulence development.

Abstract

This work is concerned with advancing multi-fluid models in General Relativity, and in particular focuses on the modelling of dissipative fluids and turbulent flows. Such models are required for an accurate description of neutron star phenomenology, and binary neutron star mergers in particular. In fact, the advent of multi-messenger astronomy offers exciting prospects for exploring the extreme physics at play during such cosmic fireworks. We first focus on modelling dissipative fluids in relativity, and explore the arguably unique model that is ideally suited for describing dissipative multi-fluids in General Relativity. Modelling single fluids in relativity is already a hard task, but for neutron stars it is easy to argue that we need to understand even more complicated settings: the presence of superfluid/superconducting mixtures, for example, means that we need to go beyond single-fluid descriptions. We then consider turbulent flows and focus on how to perform "filtering" in a curved spacetime setting. We do so as most recent turbulent models in a Newtonian setting are based on the notion of spatial filtering. As the same strategy is beginning to be applied in numerical relativity, we focus on the foundational underpinnings and propose a novel scheme for carrying out filtering, ensuring consistency with the tenets of General Relativity. Finally, we discuss two applications of relevance for binary neutron star mergers. We focus on the modelling of ($\beta$-)reactions in neutron star simulations, and provide a discussion of the magneto-rotational instability that is suited to highly dynamical environments like mergers. We focus on these two problems as reactions are expected to source the dominant dissipative contribution to the overall dynamics, while the magneto-rotational instability is considered crucial for sustaining the development of turbulence in mergers.