Lovelock's theorem revisited

被引：17

作者：

Navarro, Alberto ^{[1
]}

Navarro, Jose ^{[1
]}

机构：

[1] Univ Extremadura, Dept Math, E-06071 Badajoz, Spain

来源：

JOURNAL OF GEOMETRY AND PHYSICS | 2011年 / 61卷 / 10期

关键词：

Natural bundles; Natural tensors; Divergence-free tensors; Lovelock's gravity; EINSTEIN TENSOR;

D O I：

10.1016/j.geomphys.2011.05.004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let (X, g) be an arbitrary pseudo-Riemannian manifold. A celebrated result by D. Lovelock gives an explicit description of all second-order natural (0,2)-tensors on X that are symmetric and divergence-free. Apart from the dual metric, the Einstein tensor of g is the simplest example. In this paper, we give a short and self-contained proof of this theorem, simplifying the existing arguments by formalizing the notion of derivative of a natural tensor. (C) 2011 Elsevier B.V. All rights reserved.

引用

页码：1950 / 1956

页数：7

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