On the uniqueness of surfaces of constant spacetime mean curvature in asymptotically Schwarzschildean lightcones

Klaus Kroencke; Markus Wolff

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arXiv · 2607.11411

On the uniqueness of surfaces of constant spacetime mean curvature in asymptotically Schwarzschildean lightcones

Klaus Kroencke·Markus Wolff

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Abstract

In this paper, we address the uniqueness of surfaces of constant spacetime mean curvature in an asymptotically Schwarzschildean lightcone of mass $m>0$. We prove that there exists a unique asymptotically flat foliation by surfaces of constant spacetime mean curvature for a fairly generic notion of asymptotic flatness. This foliation has Bondi energy $m$ and vanishing Bondi linear momentum. The authors have already established the existence of such a foliation in previous work, but proven uniqueness only in a very restrictive class of surfaces. Although this restrictive class of surfaces was necessary for the construction, here we show that the foliation is a posteriori unique under significantly weaker assumptions.

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BibTeX RIS

Klaus Kroencke, Markus Wolff. 2026-07-13. On the uniqueness of surfaces of constant spacetime mean curvature in asymptotically Schwarzschildean lightcones. https://arxiv.org/abs/2607.11411

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