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Bound of the non-commutative parameter based on the gravitational measurements.
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1  University of Batna 1
Academic Editor: Lorenzo Iorio

Published: 18 February 2023 by MDPI in 2nd Electronic Conference on Universe session Gravitation and Cosmology

In this paper, we investigated the four classical tests of general relativity in the non-commutative (NC) gauge theory of gravity, using the Seiberg-Witten (SW) map and the star product, we calculate the deformed metric components ĝµν (r, Θ) of the Schwarzschild black hole. This deformed metric enables us to calculate the gravitational periastron advance of mercury, red-shift, deflection, and time delay of light in this NC spacetime. Our results for NC prediction of the gravitational deflection and time delay of light show a new behavior than the classical one. As an application, we use a typical primordial black hole to give an estimation to the NC parameter Θ, where our result shows Θphy ∼ 10 −21 m for the gravitational red-shift, deflection, and time delay of light at the final stage of inflation, and Θphy ∼ 10 −31 m for the gravitational periastron advance for some planets of our system solar.

Keywords: non-commutative gauge field theory, periastron advance, gravitational measurements, Schwarzschild black hole.