Massive Analogue of Ashtekar-CJD Action

TL;DR

This paper generalizes the Ashtekar gravity action by adding a mass-like term, resulting in a new covariant formulation that includes a cosmological constant and explores its implications for Einstein's equations.

Contribution

It introduces a massive analogue of the Ashtekar-CJD action, extending the original metric-independent formulation with a new parameter akin to a cosmological constant.

Findings

Derived a covariant Einstein equation from the new action.

Showed the geometrical quantities are determined from the non-metric action.

Established the role of the new parameter as a cosmological constant.

Abstract

The action of Ashtekar gravity have been found by Cappovilla, Jacobson and Dell. It does not depend on the metric nor the signature of the space-time. The action has a similar structure as that of a massless relativistic particle. The former is naturally generalized by adding a term analogous to a mass term of the relativistic particle. The new action possesses a constant parameter regarded as a kind of a cosmological constant. It is interesting to find a covariant Einstein equation from the action. In order to do it we will examine how the geometrical quantities are determined from the non-metric action and how the Einstein equation follows from it.