Estimating the strength of Lorentzian distribution in non-commutative geometry by solar system tests

TL;DR

This study investigates how non-commutative geometry affects classical solar system tests, constraining the non-commutative parameter using observational data and finding it to be within a range compatible with quantum gravity scales.

Contribution

It provides the first detailed analysis of non-commutative geometry effects on solar system tests and constrains the non-commutative parameter using observational data.

Findings

Non-commutative parameter affects planetary precession more than light deflection.

The constrained non-commutative parameter is within rac{1}{2} of the Planck length.

The parameter range exceeds the Planck scale, indicating potential quantum gravity implications.

Abstract

In this paper, we study four classical tests of Schwarzschild space-time with Lorentzian distribution in non-commutative geometry. We performed detailed calculations of the first-order corrections induced by the non-commutative parameter on planetary orbital precession, light deflection, radar wave delay, and gravitational redshift. The study showed that the impact of the non-commutative parameter on the time-like geodesics is significantly greater than its effect on the null geodesics. By using a series of precise experimental observations, the allowable range for the non-commutative parameter is ultimately constrained within $\Theta\leq0.067579~\mathrm{m}^{2}$, which is given by Mercury's orbital precession. This result aligns with the view that $\sqrt{\Theta}$ is of the order of the Planck length. Moreover, this constrained parameter range exceeds the Planck scale by a significant margin.