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Advances in Mathematical Physics
Volume 2016, Article ID 1037849, 8 pages
http://dx.doi.org/10.1155/2016/1037849
Research Article

Einstein Geometrization Philosophy and Differential Identities in PAP-Geometry

1Astronomy Department, Faculty of Science, Cairo University, Giza, Egypt
2Egyptian Relativity Group, Cairo University, Giza 12613, Egypt
3Mathematics Department, Faculty of Science, Cairo University, Giza, Egypt
4Centre for Theoretical Physics, The British University in Egypt, P.O. Box 43, Cairo 11837, Egypt

Received 8 May 2016; Accepted 11 October 2016

Academic Editor: Manuel De León

Copyright © 2016 M. I. Wanas et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The importance of Einstein’s geometrization philosophy, as an alternative to the least action principle, in constructing general relativity (GR), is illuminated. The role of differential identities in this philosophy is clarified. The use of Bianchi identity to write the field equations of GR is shown. Another similar identity in the absolute parallelism geometry is given. A more general differential identity in the parameterized absolute parallelism geometry is derived. Comparison and interrelationships between the above mentioned identities and their role in constructing field theories are discussed.