On the choice of a conformal Gauss gauge near the cylinder representing spatial infinity

Abstract

A convenient approach to analyze spatial infinity is to use a cylinder representation $I$ and impose a gauge based on a congruence of conformal geodesics. This so-called conformal Gauss gauge comes along with the freedom to specify initial data for the conformal geodesics. Such a gauge has been constructed from an ordinary Cauchy surface and from past null infinity ${\mathcal{J}}^{-}$, respectively. The purpose of this note is to compare these gauges near the critical set $I^{-}$, where $I$ "touches" ${\mathcal{J}}^{-}$, as it turns out that they are related in a somewhat unexpected intricate way.

arXiv comment38 pages

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Cited by in corpus (1)

• Fully pseudospectral solution of the conformally invariant wave equation on a Kerr background