Euler observers in geometrodynamics

TL;DR

This paper introduces a new tetrad-based algorithm for evolving Cauchy surfaces in Einstein-Maxwell spacetimes, leveraging Euler observers and simplifying properties of tetrads to improve geometrodynamics analysis.

Contribution

It develops a novel tetrad framework for Cauchy evolution in curved Einstein-Maxwell spacetimes, enhancing existing algorithms with new simplifying features.

Findings

New tetrad vectors for Einstein-Maxwell geometries

Algorithm for Cauchy evolution with improved properties

Simplified analysis of spacetime evolution

Abstract

Euler observers are a fundamental tool for the study of spacetime evolution. Cauchy surfaces are evolved through the use of hypersurface orthogonal fields and their relationship to coordinate observers, that enable the use of already developed algorithms. In geometrodynamics new tetrad vectors have been introduced with outstanding simplifying properties. We are going to use these already introduced tetrad vectors in the case where we consider a curved four dimensional Lorentzian spacetime with the presence of electromagnetic fields. These Einstein-Maxwell geometries will provide the new tetrad that we are going to use in order to develop an algorithm to produce Cauchy evolution with additional simplifying properties.