KOPS - The Institutional Repository of the University of Konstanz

How to smooth a crinkled map of space-time : Uhlenbeck compactness for L<sup>∞</sup> connections and optimal regularity for general relativistic shock waves by the Reintjes-Temple equations

How to smooth a crinkled map of space-time : Uhlenbeck compactness for L connections and optimal regularity for general relativistic shock waves by the Reintjes-Temple equations

Cite This

Files in this item

Files Size Format View

There are no files associated with this item.

REINTJES, Moritz, Blake TEMPLE, 2020. How to smooth a crinkled map of space-time : Uhlenbeck compactness for L connections and optimal regularity for general relativistic shock waves by the Reintjes-Temple equations. In: Proceedings of the Royal Society of London, Series A : Mathematical, Physical and Engineering Sciences. Royal Society of London. 476(2241), 20200177. ISSN 1364-5021. eISSN 1471-2946. Available under: doi: 10.1098/rspa.2020.0177

@article{Reintjes2020-09smoot-51596, title={How to smooth a crinkled map of space-time : Uhlenbeck compactness for L connections and optimal regularity for general relativistic shock waves by the Reintjes-Temple equations}, year={2020}, doi={10.1098/rspa.2020.0177}, number={2241}, volume={476}, issn={1364-5021}, journal={Proceedings of the Royal Society of London, Series A : Mathematical, Physical and Engineering Sciences}, author={Reintjes, Moritz and Temple, Blake}, note={Article Number: 20200177} }

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<sup>p</sup> spaces. The theory and results announced in this paper apply to arbitrary L<sup>∞</sup> connections on the tangent bundle TM of arbitrary manifolds M, including Lorentzian manifolds of general relativity. Temple, Blake 2020-11-03T07:09:40Z Reintjes, Moritz 2020-09 Temple, Blake eng Reintjes, Moritz How to smooth a crinkled map of space-time : Uhlenbeck compactness for L<sup>∞</sup> connections and optimal regularity for general relativistic shock waves by the Reintjes-Temple equations 2020-11-03T07:09:40Z

This item appears in the following Collection(s)

Search KOPS


Browse

My Account