Limits of the Energy-Momentum Tensor in General Relativity

A limiting diagram for the Segre classification of the energy-momentum tensor is obtained and discussed in connection with a Penrose specialization diagram for the Segre types. A generalization of the coordinate-free approach to limits of Paiva et al. to include non-vacuum space-times is made. Geroch's work on limits of space-times is also extended. The same argument also justifies part of the procedure for classification of a given spacetime using Cartan scalars. pacs numbers: 04.20.-q 04.20.Cv 04.20.Jb 1 Introduction The matter content in general relativity theory is described by a second order symmetric tensor, the energy-momentum tensor. Under limiting processes, one would like to know which energy-momentum tensors might arise. A step in this study is the investigation of the limits of classes of energy-momentum tensors. Departamento F'isica Te'orica, Universidade do Estado do Rio de Janeiro, Rua S~ao Francisco Xavier 524 (Maracan~a), 20550-013 Rio de Janeiro - RJ, Brasil, inte..