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Weyl curvature evolution system for GR

Krasnov, Kirill; Shaw, Adam

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Authors

KIRILL KRASNOV kirill.krasnov@nottingham.ac.uk
Professor of Mathematical Sciences

Adam Shaw



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 Mar 29, 2024
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.

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