Adaptive mesh and geodesically sliced Schwarzschild spacetime in 3+1 dimensions

TL;DR

This paper introduces a 3+1 dimensional adaptive mesh code for numerical general relativity, demonstrating its application to evolving a Schwarzschild spacetime with geodesic slicing, highlighting its potential for flexible and efficient simulations.

Contribution

It presents the first results of an adaptive mesh implementation in 3+1 dimensional numerical relativity for Schwarzschild spacetime evolution.

Findings

Adaptive mesh enhances numerical efficiency.

Effective evolution of Schwarzschild spacetime with geodesic slicing.

Supports use of coordinate patches in numerical relativity.

Abstract

We present first results obtained with a 3+1 dimensional adaptive mesh code in numerical general relativity. The adaptive mesh is used in conjunction with a standard ADM code for the evolution of a dynamically sliced Schwarzschild spacetime (geodesic slicing). We argue that adaptive mesh is particularly natural in the context of general relativity, where apart from adaptive mesh refinement for numerical efficiency one may want to use the built in flexibility to do numerical relativity on coordinate patches.