Toward astrophysics applications of causal, stable relativistic dissipative hydrodynamics

Abstract

Fluid mechanics has proven to be remarkably successful in describing a wide variety of substances, both familiar and exotic. The latter category includes relativistic fluids, often arising in the most extreme regimes found anywhere in the universe. One such example is the quark-gluon plasma (QGP) formed in collisions of heavy ions, which exists at temperatures hot enough to “melt” hadrons; another is the matter composing neutron stars, whose density is comparable to that of an atomic nucleus. Beyond the surprising fact that the aforementioned substances act as fluids, they share an additional similarity in that they may both be measurably viscous, a feature accounted for in models of the QGP but almost never in astrophysical contexts such as the neutron star. In this thesis I present progress toward the incorporation of dissipative effects into fluid models of relativistic astrophysical systems. Toward this end, my collaborators and I have made use of a novel theoretical framework developed by Bemfica, Disconzi, Noronha, and Kovtun referred to as BDNK theory, which we argue is the only relativistic dissipative fluid theory with a mathematical foundation suitable for the applications of interest. We present the first nonlinear numerical solutions to the BDNK PDEs and analyze their properties, develop a conservative finite volume numerical scheme for them, and present a formulation of the equations with astrophysically relevant microphysics. Building upon these works, we present preliminary results for the first application of BDNK theory to neutron stars, in the context of radial stellar oscillations.