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We calculate leading long-distance noncommutative corrections to the classical Schwarzschild black hole sourced by a massive noncommutative scalar field. The energy-momentum tensor is taken O(⁴) in the noncommutative parameter and is treated in the semiclassical (tree-level) approximation. These noncommutative corrections dominate classical post-post-Newtonian corrections if >1/MP. However, they are still very small to be observable in present-day experiments.
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Archil Kobakhidze (2009) studied this question.
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