General relativistic smoothed particle hydrodynamics

Abstract

We present a method for general relativistic smoothed particle hydrodynamics\n(GRSPH), based on an entropy-conservative form of the general relativistic\nhydrodynamic equations for a perfect fluid. We aim to replace approximate\ntreatments of general relativity in current SPH simulations of tidal disruption\nevents and accretion discs. We develop an improved shock capturing formulation\nthat distinguishes between shock viscosity and conductivity in relativity. We\nalso describe a new Hamiltonian time integration algorithm for relativistic\norbital dynamics and GRSPH. Our method correctly captures both Einstein and\nspin-induced precession around black holes. We benchmark our scheme in 1D and\n3D against mildly and ultra relativistic shock tubes, exact solutions for\nepicyclic and vertical oscillation frequencies, and Bondi accretion. We assume\nfixed background metrics (Minkowski, Schwarzschild and Kerr in Cartesian\nBoyer-Lindquist coordinates) but the method lays the foundation for future\ndirect coupling with numerical relativity.\n