Scalar conformal invariants of weight zero
Abstract
In the class of metrics of a generic conformal structure there exists a distinguishing metric. This was noticed by Albert Einstein in a lesserknown paper of 1921 (Berl. Ber., 1921, pp. 261264). We explore this finding from a geometrical point of view. Then, we obtain a family of scalar conformal invariants of weight 0 for generic pseudoRiemannian conformal structures $[g]$ in more than three dimensions. In particular, we define the conformal scalar curvature of $[g]$ and calculate it for some wellknown 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.
 Publication:

arXiv eprints
 Pub Date:
 September 2017
 arXiv:
 arXiv:1709.06798
 Bibcode:
 2017arXiv170906798S
 Keywords:

 Mathematics  Differential Geometry;
 General Relativity and Quantum Cosmology;
 53A55;
 53A30;
 83C05
 EPrint:
 This work was presented for the first time at the SpanishPortuguese Relativity Meeting  EREP 2017 held in M\'alaga (Spain), 1215 September 2017. 5 pages, 1 table