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Microlocal analysis
near null infinity in asymptotically flat spacetimes
Peter Hintz and András Vasy |
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Vol. 19 (2026), No. 1, 1–106
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Abstract |
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We present a novel approach to the analysis of regularity and decay for solutions of wave equations in a neighborhood of null infinity in asymptotically flat spacetimes of any dimension. The classes of metrics and wave-type operators we consider near null infinity include those arising in nonlinear stability problems for Einstein’s field equations in dimensions. In a neighborhood of null infinity, in an appropriate compactification of the spacetime to a manifold with corners, the wave operators are of edge type at null infinity and totally characteristic at spacelike and future timelike infinity. On a corresponding scale of Sobolev spaces, we demonstrate how microlocal regularity propagates across or into null infinity via a sequence of radial sets. As an application, inspired by work of the second author with Baskin and Wunsch, we prove regularity and decay estimates for forward solutions of wave-type equations on asymptotically flat spacetimes which are asymptotically homogeneous with respect to scaling in the forward timelike cone and have an appropriate structure at null infinity. These estimates are new even for the wave operator on Minkowski space. The results obtained here are also used as black boxes in a global theory of wave-type equations on asymptotically flat and asymptotically stationary spacetimes developed by the first author. |
Keywords
wave equation, asymptotically flat spacetimes, null
infinity, microlocal analysis, edge operators, totally
characteristic operators, null-bicharacteristic flow,
propagation estimates, radial sets
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Mathematical Subject Classification
Primary: 35L05
Secondary: 35B40, 58J47
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Milestones
Received: 2 May 2023
Revised: 30 September 2024
Accepted: 8 January 2025
Published: 26 November 2025
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Authors |
| Peter Hintz | |
| Department of Mathematics ETH Zürich Zürich Switzerland |
Department of Mathematics Pennsylvania State University State College, PA United States |
| András Vasy | |
| Department of Mathematics Stanford University Stanford, CA United States |
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| © 2026 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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