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. 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.

中文翻译：

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从光的弯曲到正质量：非 PDE 视角

彭罗斯等人。通过光的弯曲研究了具有负质量的时空的物理不相干性。需要对零测地线的时间延迟进行精确估计，并在他们的证明中发挥了关键作用。在本文中，我们构建了一个中间对角线度量，并将这个问题简化为紧致时空中关于共形无穷附近的类时连通性的因果关系比较。这种不同的方法使我们能够避免遇到 Penrose等人提出的困难和微妙问题。遇见了。它提供了一种新的、基本简单且物理上自然的非偏微分方程观点来理解正质量定理。这个基本论点适度地适用于真空且接近无穷大的渐近平坦解。