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Probing spacetime noncommutative constant via charged astrophysical black hole lensing

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Abstract

We study the influence of the spacetime noncommutative parameter on the strong field gravitational lensing in the noncommutative Reissner-Nordström black-hole spacetime. Supposing that the gravitational field of the supermassive central object of the Galaxy is described by this metric, we estimate the numerical values of the coefficients and observables for strong gravitational lensing. Our results show that with the increase of the parameter \( \sqrt {\vartheta } \), the observables θ ∞ and r m decrease, while s increases. Our results also show that i) if \( \sqrt {\vartheta } \) is strong, the observables are close to those of the noncommutative Schwarzschild black hole lensing; ii) if \( \sqrt {\vartheta } \) is weak, the observables are close to those of the commutative Reissner-Nordström black hole lensing; iii) the detectable scope of ϑ in a noncommutative Reissner-Nordström black hole lensing is \( 0.12 \leq \sqrt {\vartheta } \leq 0.26 \), which is wider than that in a noncommutative Schwarzschild black hole lensing, \( 0.18 \leq \sqrt {\vartheta } \leq 0.26 \). This may offer a way to probe the spacetime noncommutative constant ϑ by the astronomical instruments in the future.

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  1. Department of Physics and Information Engineering, Hunan Institute of Humanities, Science and Technology, Loudi, Hunan, 417000, China

    Chikun Ding

  2. Department of Physics, and Key Laboratory of Low Dimensional Quantum Structures and Quantum Control of Ministry of Education, Hunan Normal University, Changsha, Hunan, 410081, China

    Jiliang Jing

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Ding, C., Jing, J. Probing spacetime noncommutative constant via charged astrophysical black hole lensing. J. High Energ. Phys. 2011, 52 (2011). https://doi.org/10.1007/JHEP10(2011)052

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