Numerical Black Holes: A Moving Grid Approach

TL;DR

This paper presents a finite difference numerical relativity code for spherically symmetric black holes, extending it to moving grids to improve accuracy near horizons, addressing errors caused by steep gradients.

Contribution

It introduces a moving grid approach in numerical relativity to better model black hole horizons and reduce errors from steep gradients.

Findings

Errors in mass function due to steep gradients are significant.

Moving grids improve the accuracy of black hole exterior modeling.

The formalism extends to hyperbolic Einstein equations with harmonic slicing.

Abstract

Spherically symmetric (1D) black-hole spacetimes are considered as a test for numerical relativity. A finite difference code, based in the hyperbolic structure of Einstein's equations with the harmonic slicing condition is presented. Significant errors in the mass function are shown to arise from the steep gradient zone behind the black hole horizon, which challenge the Computational Fluid Dynamics numerical methods used in the code. The formalism is extended to moving numerical grids, which are adapted to follow horizon motion. The black hole exterior region can then be modeled with higher accuracy.