Conformally covariant systems of wave equations and their equivalence to\n Einstein's field equations

2013/06/26 by Tim-Torben Paetz, Paetz, Tim-Torben
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Nonlinear Waves and Solitons #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.1306.6204

openalex publication_date 2013/06/26 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

We derive, in 3+1 spacetime dimensions, two alternative systems of\nquasi-linear wave equations, based on Friedrich's conformal field equations. We\nanalyse their equivalence to Einstein's vacuum field equations when appropriate\nconstraint equations are satisfied by the initial data. As an application, the\ncharacteristic initial value problem for the Einstein equations with data on\npast null infinity is reduced to a characteristic initial value problem for\nwave equations with data on an ordinary light-cone.\n

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