Classification Of Second Order Symmetric Tensors Research Articles

Physical structure of the energy-momentum tensor in General Relativity

The algebraic classification of second-order symmetric tensors based on Segre type is used to give a systematic description of energy-momentum tensors in General Relativity. The uniqueness of the physical interpretation of a given energy-momentum tensor is discussed algebraically and a brief description of their “inheritance of symmetry” properties is also given.

Spinors, algebraic geometry, and the classification of second-order symmetric tensors in general relativity

Two approaches to the problem of classifying second-order symmetric tensors in space-time given by Ludwig and Scanlon and by Penrose are discussed. Ludwig and Scanlon use both spinor and tensor algebra in their approach, whereas Penrose uses spinors and the properties of certain curves in complex projective 3-space. These approaches yield essentially identical classifications, and this paper points out the connections between them in detail and tabulates the results.