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arXiv · 2602.05061

Transverse expansion of the metric at null infinity

Marc Mars·Gabriel Sánchez-Pérez
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Abstract

In this paper we analyze the conformal Einstein equations to all orders at null infinity without imposing any restriction on the spacetime dimension, the topology of $\mathscr{I}$, or fall-off conditions for the Weyl tensor. In particular, we study how the equations constrain the geometry of null infinity when it is assumed to be foliated by cross-sections, not necessarily spheres. Our approach is coordinate-free and treats the conformal factor $\Omega$ as a dynamical variable. After identifying the free data at $\mathscr{I}$, we show that any two asymptotically flat spacetimes sharing the same free data at null infinity are necessarily isometric to infinite order. In addition, we provide a detached definition of null infinity and prove an existence theorem for asymptotically flat spacetimes solving the field equations to infinite order at $\mathscr{I}$ realizing the prescribed initial data.

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Marc Mars, Gabriel Sánchez-Pérez. 2026-02-04. Transverse expansion of the metric at null infinity. https://arxiv.org/abs/2602.05061

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