Rigidity for Lorentzian metrics with the same length of null-geodesics

2022/05/12 by Gregory Eskin, Eskin, Gregory
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2205.05860

openalex publication_date 2022/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the Lorentzian metric independent of the time variable in the cylinder ℝ×Ω where x₀∈ℝ is the time variable and Ω is a bounded smooth domain in ℝⁿ. We consider forward null-geodesics in ℝ× Ω starting on ℝ×∂Ω at t=0 and leaving ℝ×Ω at some later time. We prove the following rigidity result: If two Lorentzian metrics are close enough in some norm and if corresponding null-geodesics have equal lengths then the metrics are equal.

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