  We present a solution of the coupled Einstein and rank-two antisymmetric
tensor field equations where Lorentz symmetry is spontaneously broken, and we
discuss its observational signatures. Especially, the deflection angles have
important qualitative differences between tensor and scalar monopoles. If a
monopole were to be detected, it would be discriminated whether or not to
correspond to a tensor one. This phenomenon might open up new direction in the
search of Lorentz violation with future astrophysical observations.
