Strong gravitational lensing in a noncommutative black-hole spacetime
  Noncommutative geometry may be a starting point to a quantum gravity. We
study the influence of the spacetime noncommutative parameter on the strong
field gravitational lensing in the noncommutative Schwarzschild black-hole
spacetime and obtain the angular position and magnification of the relativistic
images. Supposing that the gravitational field of the supermassive central
object of the galaxy described by this metric, we estimate the numerical values
of the coefficients and observables for strong gravitational lensing. Comparing
to the Reissner-Norstr\"{om} black hole, we find that the influences of the
spacetime noncommutative parameter is similar to those of the charge, just
these influences are much smaller. This may offer a way to distinguish a
noncommutative black hole from a Reissner-Norstr\"{om} black hole, and may
probe the spacetime noncommutative constant $\vartheta$ \cite{foot} by the
astronomical instruments in the future.
