  I discuss the possibility of topological defect solutions in field theories
containing a tensor field which spontaneously breaks Lorentz symmetry. I find
that for theories of a tensor with rank r <= 5 and for which the vacuum
manifold consists of the tensors whose "square" is some constant value, only
three types of tensor (vectors, antisymmetric two-tensors, and symmetric
two-tensors) have the appropriate vacuum manifold topology to support
topological defects. Of these, topological defect solutions can be easily
constructed for two: vector domain wall solutions and antisymmetric tensor
monopole solutions. These antisymmetric tensor monopole solutions are in
principle detectible via their gravitational lensing effects.
