Probing spacetime noncommutative constant via charged astrophysical black hole lensing

Details Probing spacetime noncommutative constant via charged astrophysical black hole lensing Probing spacetime noncommutative constant via charged astrophysical black hole lensing

2011-06-10

arxiv.org/abs/1106.1974v2

JHEP10(2011)052

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

17 pages, 7 figures, 4 tables, to appear in JHEP

Scientific paper

10.1007/JHEP10(2011)052

We study the influence of the spacetime noncommutative parameter on the strong field gravitational lensing in the noncommutative Reissner-Nordstr\"{o}m 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 $\theta_{\infty}$ 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-Nordstr\"{o}m black hole lensing; iii) the detectable scope of $\vartheta$ in a noncommutative Reissner-Nordstr\"{o}m black hole lensing is $0.12\leq\sqrt{\vartheta}\leq0.26$, which is wider than that in a noncommutative Schwarzschild black hole lensing, $0.18\leq\sqrt{\vartheta}\leq0.26$. This may offer a way to probe the spacetime noncommutative constant $\vartheta$ by the astronomical instruments in the future.

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