Teleparallel Complex Gravity as Foundation for Noncommutative Gravity

TL;DR

This paper develops a teleparallel complex gravity framework that serves as a basis for noncommutative gravity, eliminating ghosts and passing classical tests, thus providing a promising foundation for quantum gravity models.

Contribution

It introduces a novel teleparallel complex gravity formulation that removes ghosts and supports noncommutative gravity, with a corresponding lagrangian proposal.

Findings

Elimination of negative energy ghosts in the gravity model

Successful passing of Mercury's perihelion test

Proposal of a lagrangian for noncommutative teleparallel gravity

Abstract

We present a teleparallel complex gravity as the foundation for the formulation of noncommutative gravity theory. The negative energy ghosts in the conventional formulation with U(1,3) local Lorentz connection no longer exists, since the local Lorentz invariance is broken down to U(1,3) global Lorentz symmetry. As desired, our teleparallel complex gravity theory also passes the key classical test of perihelion advance of Mercury. Based on this result, we present a lagrangian for the noncommutative teleparallel gravity theory.