  We present a particular solution to the Einstein field equations that could
arise as a magnetic monopole in the strong field limit of the Born-Infeld
electrodynamics. We solve its geodesics exactly and show that they can mimic
the gravitational lensing of a singular isothermal sphere, but with matter and
radiation following the same trajectories. This solution has previously been
called "cloud of strings" or "string hedgehog," and has appeared as the limit
of a global O(3) monopole.
