Scalar conformal invariants of weight zero

arXiv1709.06798MaRDI QIDQ6291577

I. Sánchez Rodríguez

Publication date: 20 September 2017

Abstract: In the class of metrics of a generic conformal structure there exists a distinguishing metric. This was noticed by Albert Einstein in a lesser-known paper of 1921 (Berl. Ber., 1921, pp. 261-264). We explore this finding from a geometrical point of view. Then, we obtain a family of scalar conformal invariants of weight 0 for generic pseudo-Riemannian conformal structures $[g]$ in more than three dimensions. In particular, we define the conformal scalar curvature of $[g]$ and calculate it for some well-known conformal spacetimes, comparing the results with the Ricci scalar and the Kretschmann scalar. In the cited paper, Einstein also announced that it is possible to add an scalar equation to the field equations of General Relativity.

Mathematics Subject Classification ID

Einstein's equations (general structure, canonical formalism, Cauchy problems) (83C05) Differential invariants (local theory), geometric objects (53A55)

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