Applications of the lichnerowicz Laplacian to stress energy tensors

AIMS Mathematics

Paul Bracken¹ 

关键词: : ;    Basis;    tensor;    connection;    differential system;    Laplacian;    bundle;    harmonic map;   

DOI  :  10.3934/Math.2017.2.545

学科分类：数学（综合）

来源: AIMS Press

【 摘 要 】

A generalization of the Laplacian for p-forms to arbitrary tensors due to Lichnerowicz will be applied to a 2-tensor which has physical applications. It is natural to associate a divergencefree symmetric 2-tensor to a critical point of a specific variational problem and it is this 2-tensor that is studied. Numerous results are obtained for the stress-energy tensor, such as its divergence and Laplacian. A remarkable integral formula involving a symmetric 2-tensor and a conformal vector field is obtained as well.

【 授权许可】

CC BY