Numerical evolution of matter in dynamical axisymmetric black hole spacetimes. I. Methods and tests

TL;DR

This paper presents a new numerical code for simulating matter evolution in axisymmetric black hole spacetimes, incorporating advanced hydrodynamics and spacetime evolution techniques, validated through comprehensive tests and applications.

Contribution

It introduces a novel numerical framework combining high-resolution shock-capturing hydrodynamics with axisymmetric spacetime evolution for black hole scenarios.

Findings

Successful simulation of matter accretion onto black holes

Validation of the code with new testbed calculations

Insights into matter behavior and horizon dynamics in black hole spacetimes

Abstract

We have developed a numerical code to study the evolution of self-gravitating matter in dynamic black hole axisymmetric spacetimes in general relativity. The matter fields are evolved with a high-resolution shock-capturing scheme that uses the characteristic information of the general relativistic hydrodynamic equations to build up a linearized Riemann solver. The spacetime is evolved with an axisymmetric ADM code designed to evolve a wormhole in full general relativity. We discuss the numerical and algorithmic issues related to the effective coupling of the hydrodynamical and spacetime pieces of the code, as well as the numerical methods and gauge conditions we use to evolve such spacetimes. The code has been put through a series of tests that verify that it functions correctly. Particularly, we develop and describe a new set of testbed calculations and techniques designed to handle dynamically sliced, self-gravitating matter flows on black holes, and subject the code to these tests. We make some studies of the spherical and axisymmetric accretion onto a dynamic black hole, the fully dynamical evolution of imploding shells of dust with a black hole, the evolution of matter in rotating spacetimes, the gravitational radiation induced by the presence of the matter fields and the behavior of apparent horizons through the evolution.