Abstract

The Bakry-Émery Ricci tensor gives an analogue of the Ricci tensor for a Riemannian manifold with a smooth function. This notion motivates a new version of Einstein’s field equation in which the mass becomes part of geometry. This new field equation is purely geometric and is obtained from an action principle which is formed naturally by the scalar curvature associated with the Bakry-Émery Ricci tensor.

中文翻译：

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Bakry-ÉmeryRicci张量：在时空质量分布中的应用

摘要

Bakry-ÉmeryRicci张量给出了具有光滑函数的黎曼流形的Ricci张量的类似物。这个概念激发了爱因斯坦场方程的新版本，其中质量成为几何的一部分。这个新的场方程纯粹是几何的，是从作用原理获得的，该作用原理自然是由与Bakry-ÉmeryRicci张量相关的标量曲率形成的。