Please use this identifier to cite or link to this item: http://repositorio.unicamp.br/jspui/handle/REPOSIP/54296
Type: Artigo de periódico
Title: An ambiguous statement called the "tetrad postulate" and the correct field equations satisfied by the tetrad fields
Author: Rodrigues, WA
Souza, QAG
Abstract: The names tetrad, tetrads, cotetrads have been used with many different meanings in the physics literature, not all of them equivalent from the mathematical point of view. In this paper, we introduce unambiguous definitions for each of those terms, and show how the old miscellanea made many authors introduce in their formalism an ambiguous statement called the "tetrad postulate," which has been the source of much misunderstanding, as we show explicitly by examining examples found in the literature. Since formulating Einstein's field equations intrinsically in terms of cotetrad fields theta(a), a = 0, 1, 2, 3 is a worthy enterprise, we derive the equation of motion of each theta(a) using modern mathematical tools (the Clifford bundle formalism and the theory of the square of the Dirac operator). Indeed, we identify (giving all details and theorems) from the square of the Dirac operator some noticeable mathematical objects, namely, the Ricci, Einstein, co-variant D'Alembertian and the Hodge Laplacian operators, which permit us to show that each theta(a) satisfies a well-defined wave equation. Also, we present for completeness a detailed derivation of the cotetrad wave equations from a variational principle. We compare the cotetrad wave equation satisfied by each theta(a) with some others appearing in the literature, and which are unfortunately in error.
Subject: tetrads
"tetrad postulate"
Ricci and Einstein operators
Einstein equations in tetrad form
Country: Singapura
Editor: World Scientific Publ Co Pte Ltd
Rights: fechado
Identifier DOI: 10.1142/S0218271805008157
Date Issue: 2005
Appears in Collections:Artigos e Materiais de Revistas Científicas - Unicamp

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