Gravity Equivalent to Teleparallelism: Some Basic Geometrical Aspects

TL;DR

This paper reviews Teleparallel Gravity, an alternative formulation of gravity using torsion instead of curvature, highlighting its differences, advantages, and mathematical properties compared to General Relativity.

Contribution

It provides a concise overview of Teleparallel Gravity, emphasizing its geometric aspects and comparing it with the traditional curvature-based approach of General Relativity.

Findings

Teleparallel Gravity uses torsion instead of curvature to describe gravity.

It highlights advantages of Teleparallel Gravity over General Relativity.

Discusses properties of the Weintzenb"ock connection.

Abstract

We review the book of Ruben Aldrovandi and Jose Geraldo Pereira about Teleparallel Gravity. Teleparallel Gravity is an alternative to General Relativity to describe the gravitational interaction. The difference between General Relativity and Teleparallel Gravity is the fact that General Relativity associates the curvature to the gravitational interaction, whereas in the Teleparallel Gravity the mathematical object associated to gravitational field is the torsion, whose field is the so called Weintzenb\"ock connection. We discuss briefly the advantages of Teleparallel Gravity over General Relativity as well as Weintzenb\"ock connection properties.