A Connection Approach to Numerical Relativity

TL;DR

This paper introduces a novel formalism for numerical relativity that uses the Ashtekar connection and Newman-Penrose scalars as dynamical variables, addressing gauge and reality constraints in complex spacetime evolutions.

Contribution

It presents a new approach to numerical relativity employing connection and scalar variables, with specific gauge choices for Petrov type 1111 spacetimes.

Findings

Identified a suitable gauge with constant spatial volume element

Developed a formalism handling gauge constraints and reality conditions

Applied method to a specific Petrov type spacetime

Abstract

We discuss a general formalism for numerically evolving initial data in general relativity in which the (complex) Ashtekar connection and the Newman-Penrose scalars are taken as the dynamical variables. In the generic case three gauge constraints and twelve reality conditions must be solved. The analysis is applied to a Petrov type \{1111\} planar spacetime where we find a spatially constant volume element to be an appropriate coordinate gauge choice.