Einstein Geometrization Philosophy and Differential Identities in PAP-Geometry

TL;DR

This paper explores Einstein's geometrization philosophy, emphasizing the role of differential identities like Bianchi and their generalizations in formulating gravitational theories beyond general relativity.

Contribution

It introduces a new differential identity in parameterized absolute parallelism geometry and discusses its implications for constructing field theories.

Findings

Derivation of a generalized differential identity in PAP-geometry.

Clarification of the role of differential identities in Einstein's geometrization.

Comparison between identities in different geometric frameworks.

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.