Generalized Chern-Simons action principles for gravity

TL;DR

This paper introduces generalized differential forms and connections to formulate Chern-Simons action principles that yield Einstein's vacuum equations, providing a novel geometric approach to gravity.

Contribution

It develops generalized Chern-Simons actions based on generalized connections that reproduce Einstein's vacuum equations as their Euler-Lagrange equations.

Findings

Connections lead to Lorentzian metrics satisfying Einstein's vacuum equations

Constructs generalized Chern-Simons actions with Einstein's equations as Euler-Lagrange equations

Provides a geometric framework for gravity using generalized differential forms

Abstract

Generalized differential forms are employed to construct generalized connections. Lorentzian four-metrics determined by certain of these connections satisfy Einstein's vacuum field equations when the connections are flat. Generalized Chern-Simons action principles with Einstein's equations as Euler-Lagrange equations are constructed by using these connections.