On the naturalness of Einstein's equation

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On the naturalness of Einstein's equation

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Title: On the naturalness of Einstein's equation
Author: Navarro Garmendia, José; Sancho de Salas, Juan Bautista
Abstract: Calculamos los tensores 2-covariantes construidos naturalmente a partir de una métrica semi-riemanniana los cuales están libres de divergencia y tienen un peso mayor que -2. Como consecuencia, se deduce una caracterización del tensor de Einstein como la única, hasta un factor constante, tensor 2-covariante construido naturalmente de una métrica semi-Riemann la cual es libre de divergencia y tiene un peso 0 (es decir, es independiente de la unidad de la escala). Dado que estas dos condiciones también son satisfechas por el tensor de energía-impulso de un espacio-tiempo relativista, se discute en detalle cómo estos teoremas conducen a la ecuación de campo de la Relatividad General.We compute all 2-covariant tensors naturally constructed from a semiriemannian metric g which are divergence-free and have weight greater than −2. As a consequence, it follows a characterization of the Einstein tensor as the only, up to a constant factor, 2-covariant tensor naturally constructed from a semiriemannian metric which is divergence-free and has weight 0 (i.e., is independent of the unit of scale). Since these two conditions are also satisfied by the energy-momentum tensor of a relativistic space-time, we discuss in detail how these theorems lead to the field equation of General Relativity.
Description: Publicado en: J Geom. Phys. 58, 8 (2008) 1007-1014 DOI: 10.1016/j.geomphys.2008.03.007
URI: http://hdl.handle.net/10662/2565
Date: 2007-10


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