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arXiv · 2411.06628

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

Rui-Bo Wang·Shi-Jie Ma·Jian-Bo Deng·Xian-Ru Hu
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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.

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Rui-Bo Wang, Shi-Jie Ma, Jian-Bo Deng, Xian-Ru Hu. 2024-11-10. Estimating the strength of Lorentzian distribution in non-commutative geometry by solar system tests. https://doi.org/10.1142/s0217732325500348

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