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- W3084531312 abstract "We present the authors’ new theory of the RT-equations (‘regularity transformation’ or ‘Reintjes–Temple’ equations), nonlinear elliptic partial differential equations which determine the coordinate transformations which smooth connections Γ to optimal regularity, one derivative smoother than the Riemann curvature tensor Riem( Γ ). As one application we extend Uhlenbeck compactness from Riemannian to Lorentzian geometry; and as another application we establish that regularity singularities at general relativistic shock waves can always be removed by coordinate transformation. This is based on establishing a general multi-dimensional existence theory for the RT-equations by application of elliptic regularity theory in L p spaces. The theory and results announced in this paper apply to arbitrary L ∞ connections on the tangent bundle <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML overflow=scroll> <mml:mi>T</mml:mi> <mml:mrow> <mml:mrow> <mml:mi mathvariant=script>M</mml:mi> </mml:mrow> </mml:mrow> </mml:math> of arbitrary manifolds <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML overflow=scroll> <mml:mrow> <mml:mrow> <mml:mi mathvariant=script>M</mml:mi> </mml:mrow> </mml:mrow> </mml:math> , including Lorentzian manifolds of general relativity." @default.
- W3084531312 created "2020-09-21" @default.
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- W3084531312 date "2020-09-01" @default.
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- W3084531312 title "How to smooth a crinkled map of space–time: Uhlenbeck compactness for <i>L</i> <sup>∞</sup> connections and optimal regularity for general relativistic shock waves by the Reintjes–Temple equations" @default.
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- W3084531312 doi "https://doi.org/10.1098/rspa.2020.0177" @default.
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