# General relativistic smoothed particle hydrodynamics

## TL;DR

This paper introduces a novel general relativistic smoothed particle hydrodynamics (GRSPH) method that accurately models relativistic fluids around black holes, incorporating shock capturing, Hamiltonian integration, and benchmarking against known solutions.

## Contribution

The paper develops a new GRSPH framework with improved shock handling and a Hamiltonian integrator, enabling more accurate simulations of relativistic astrophysical phenomena.

## Key findings

- Successfully captures Einstein and spin precession effects.
- Accurately reproduces shock tube and accretion flow solutions.
- Demonstrates robustness in 1D and 3D relativistic tests.

## Abstract

We present a method for general relativistic smoothed particle hydrodynamics (GRSPH), based on an entropy-conservative form of the general relativistic hydrodynamic equations for a perfect fluid. We aim to replace approximate treatments of general relativity in current SPH simulations of tidal disruption events and accretion discs. We develop an improved shock capturing formulation that distinguishes between shock viscosity and conductivity in relativity. We also describe a new Hamiltonian time integration algorithm for relativistic orbital dynamics and GRSPH. Our method correctly captures both Einstein and spin-induced precession around black holes. We benchmark our scheme in 1D and 3D against mildly and ultra relativistic shock tubes, exact solutions for epicyclic and vertical oscillation frequencies, and Bondi accretion. We assume fixed background metrics (Minkowski, Schwarzschild and Kerr in Cartesian Boyer-Lindquist coordinates) but the method lays the foundation for future direct coupling with numerical relativity.