Gravitational Constant and Torsion

TL;DR

This paper explores the relationship between the topological Nieh-Yan density in Riemann-Cartan spacetime and the gravitational constant, deriving the Einstein-Hilbert Lagrangian from this connection.

Contribution

It demonstrates how linking the Nieh-Yan density to the gravitational constant yields the Einstein-Hilbert Lagrangian in Riemann-Cartan space.

Findings

Einstein-Hilbert Lagrangian derived from topological considerations

Connection established between Nieh-Yan density and gravitational constant

Insights into the geometric foundation of gravity

Abstract

Riemann-Cartan space time $U_{4}$ is considered here. It has been shown that when we link topological Nieh-Yan density with the gravitational constant then we get Einstein-Hilbert Lagrangian as a consequence.