Gravity in Extreme Regions Based on Noncommutative Quantization of Teleparallel Gravity

TL;DR

This paper develops a simple noncommutative gravity model based on teleparallel gravity, applying Moyal deformation and Seiberg-Witten map, and explores its implications for early universe cosmology and black hole physics.

Contribution

It introduces a novel noncommutative gravitational theory using teleparallel gravity, clarifies the roles of different products, and investigates quantum gravity effects in extreme regions.

Findings

Gravity acts repulsively in extreme quantum regions.

The model separates metric and noncommutative effects clearly.

Cosmic evolution and black hole features are analyzed within this framework.

Abstract

In this paper, a noncommutative gravitational theory is constructed by applying Moyal deformation quantization and the Seiberg-Witten map to teleparallel gravity, a classical gravitational theory, as a gauge theory of local translational symmetry. Since our model is based on teleparallel gravity, it is an extremely simple noncommutative gravitational theory. We also clearly divide the role of the products, such that the metric is responsible for the rule of the inner product (which is calculated by taking the sum over the subscripts) and the Moyal product is responsible for tensor and field noncommutativity. This solves problems related to the order of the products and the relationship between the metric and the Moyal product. Furthermore, we analyze the cosmic evolution of the very early universe and the spacetime features around black holes using the constructed noncommutative gravitational theory, and find that gravity acts repulsively in the extreme region where its quantum effects become prominent.