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From bending of light to positive mass: a non-PDE perspective. (English) Zbl 1465.83018

Summary: In [“A positive mass theorem based on the focusing and retardation of null geodesics”, Preprint, arXiv:9301015], R. Penrose et al. investigated the physical incoherence of the spacetime with negative mass via the bending of light. Precise estimates of the time-delay of null geodesics were needed and played a pivotal role in their proof. In this paper, we construct an intermediate diagonal metric and reduce this problem to a causality comparison in the compactified spacetimes regarding timelike connectedness near conformal infinities. This different approach allows us to avoid encountering the difficulties and subtle issues that Penrose et al. [loc. cit.] met. It provides a new, substantially simple, and physically natural non-partial differential equation viewpoint to understand the positive mass theorem. This elementary argument modestly applies to asymptotically flat solutions that are vacuum and stationary near infinity.
©2021 American Institute of Physics

MSC:

83C75 Space-time singularities, cosmic censorship, etc.
83C10 Equations of motion in general relativity and gravitational theory
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