Generalized forms and gravitation

TL;DR

This paper reviews generalized differential forms and constructs generalized connections, showing their relation to Einstein's vacuum equations and formulating Chern-Simons actions that yield these equations as Euler-Lagrange conditions.

Contribution

It introduces a class of generalized connections and formulates Chern-Simons actions linked to Einstein's vacuum equations.

Findings

Generalized connections include flat connections satisfying Einstein's equations.

Certain generalized Chern-Simons actions produce Einstein's vacuum equations.

The algebra of generalized forms provides a framework for gravitational theories.

Abstract

The algebra and calculus of generalized differential forms are reviewed and employed to construct a class of generalized connections and to investigate their properties. The class includes generalized connections which are flat when Einstein's vacuum field equations are satisfied. Generalized Chern-Simons action principles are formulated and it is shown that certain of these have Einstein's vacuum field equations as Euler-Lagrange equations.