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The Algebra of the Riemann Curvature Tensor in General Relativity: The Relation of the Invariants of the Einstein Curvature Tensor to the Invariants Describing Matter
Author(s) -
Greenberg Phillip
Publication year - 1972
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm1972514369
Subject(s) - ricci decomposition , riemann curvature tensor , einstein tensor , ricci curvature , mathematics of general relativity , weyl tensor , mathematics , tensor density , mathematical physics , tensor contraction , scalar curvature , tensor (intrinsic definition) , curvature , introduction to the mathematics of general relativity , stress–energy tensor , tensor calculus , general relativity , pure mathematics , mathematical analysis , tensor field , exact solutions in general relativity , geometry , numerical relativity
In this paper, the second in a series of papers on the algebra of the Riemann curvature tensor, we relate the algebraic invariants of the Einstein curvature tensor to the algebraic invariants of the trace‐free part of the Ricci tensor, and, consequently, to the trace‐free part of the stress‐energy tensor for the physical system. We also show explicitly how all of the components of the trace‐free part of the Ricci tensor transform under a Lorentz transformation.