Geodesic equation in non-commutative gauge theory of gravity

Abstract

In this work, we construct a non-commutative (NC) gauge theory of gravity for any metric with spherical symmetries, where we use a non-diagonal tetrad field. The deformed gauge potentials (tetrad fields) and the components of deformed metric are computed to the second order in the NC parameter ${\Theta }^{\mu \nu }$, as the application to the Schwarzschild black hole we show that the NC geometry removes the singularity at the origin of the black hole, and increase the event horizon. The non-commutativity correction to the effective potential of the Schwarzschild metric is also computed and we show how this geometry affects the stability condition which it found the NC parameter plays the same role as the mass that can be used to explain the dark matter and we show that the NC Schwarzschild space-time has new stable circular orbits appear near the event horizon that is not allowed by Schwarzschild space-time. The geodesic equations in the NC space and the corrections to the periastron advance in terms of $\Theta$ are obtained. We have also specified the problem of Mercury's perihelion and used the experimental data to estimate the NC parameter $\Theta$, then we show that $\Theta$ of the order $10^{-25}s.k{g}^{-1}$ gives observable corrections to the movement at a large scale. We show that the NC propriety of the spacetime appears at the High Energy.

23 pages, 18 figures

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• Thermodynamic Properties of Schwarzschild Black Hole in Non-Commutative Gauge Theory of Gravity
• Quantum tunneling from Schwarzschild black hole in non-commutative gauge theory of gravity
• Particle production induced by a Lorentzian non-commutative spacetime
• Properties of an axisymmetric Lorentzian non-commutative black hole
• Constructing noncommutative black holes
• Non-commutativity in Hayward spacetime
• Schwarzschild black hole surrounded by a cavity and phase transition in the non-commutative gauge theory of gravity
• Different Regular Black Holes: Geodesic Structures of Test Particles
• Geodesic motion of a test particle around a noncommutative Schwarzchild Anti-de Sitter black hole
• Elastic scattering of electron by a Yukawa potential in non-commutative spacetime
• Lyapunov exponents and geodesic stability of Schwarzschild black hole in the non-commutative gauge theory of gravity
• Comment on "Quantum tunneling from Schwarzschild black hole in non-commutative gauge theory of gravity"