Weyl curvature evolution system for GR

Krasnov, Kirill; Shaw, Adam

Abstract

Starting from the chiral first-order pure connection formulation of General Relativity, we put the field equations of GR in a strikingly simple evolution system form. The two dynamical fields are a complex symmetric tracefree 3 × 3 matrix Ψij, which encodes the self-dual part of the Weyl curvature tensor, as well as a spatial SO(3,C) connection A i a. The right-hand sides of the evolution equations also contain the triad for the spatial metric, and this is constructed non-linearly from the field Ψij and the curvature of the spatial connection A i a. The evolution equations for this pair are first order in both time and spatial derivatives, and so simple that they could have been guessed without a computation. They are the most natural spin two generalisations of Maxwell’s spin one equations. We also determine the modifications of the evolution system needed to enforce the ‘constraint sweeping’, so that any possible numerical violation of the constraints present becomes propagating and gets removed from the computational grid.

Citation

Krasnov, K., & Shaw, A. (2023). Weyl curvature evolution system for GR. Classical and Quantum Gravity, 40(7), Article 075013. https://doi.org/10.1088/1361-6382/acc0cc

• Journal Article Type: Article
• Acceptance Date: Mar 1, 2023
• Online Publication Date: Mar 14, 2023
• Publication Date: Apr 6, 2023
• Deposit Date: May 19, 2023
• Publicly Available Date: May 19, 2023
• Journal: Classical and Quantum Gravity
• Print ISSN: 0264-9381
• Electronic ISSN: 1361-6382
• Publisher: IOP Publishing
• Peer Reviewed: Peer Reviewed
• Volume: 40
• Issue: 7
• Article Number: 075013
• DOI: https://doi.org/10.1088/1361-6382/acc0cc
• Keywords: GR, new first-order formulation, recasting evolution equations
• Public URL: https://nottingham-repository.worktribe.com/output/17947206
• Publisher URL: https://iopscience.iop.org/article/10.1088/1361-6382/acc0cc
• Additional Information: Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 license. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.