Bound of the non-commutative parameter based on the gravitational measurements.

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 ĝ_µν (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 Θ^phy ∼ 10 ⁻²¹ m for the gravitational red-shift, deflection, and time delay of light at the final stage of inflation, and Θ^phy ∼ 10 ⁻³¹ m for the gravitational periastron advance for some planets of our system solar.