Applications of the lichnerowicz Laplacian to stress energy tensors

Abstract

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.

Keywords

• Basis| tensor| connection| differential system| Laplacian| bundle| harmonic map