Corrections to Schwarzschild Solution in Noncommutative Gauge Theory of Gravity

TL;DR

This paper derives a noncommutative deformation of the Schwarzschild solution in gauge theory of gravity, calculates the metric corrections, and assesses their observational significance, finding them too small for current detection.

Contribution

It introduces a second-order noncommutative correction to the Schwarzschild solution within gauge theory of gravity, expanding the understanding of quantum spacetime effects.

Findings

Deformed Schwarzschild metric components are explicitly calculated.

Noncommutative corrections to gravitational redshift are quantified.

Corrections are too small for current observational detection.

Abstract

A deformed Schwarzschild solution in noncommutative gauge theory of gravitation is obtained. The gauge potentials (tetrad fields) are determined up to the second order in the noncommutativity parameters $\Theta^{\mu\nu}$. A deformed real metric is defined and its components are obtained. The noncommutativity correction to the red shift test of General Relativity is calculated and it is concluded that the correction is too small to have observable effects. Implications of such a deformed Schwarzschild metric are also mentioned.