Topological Defects As Source Of Non-Trivial Metric

Topological defects in ³He-A represent the topologically stable configurations of the order parameter. Since some components of the order parameter serve as the metric field of effective gravity, one can use the defects as the source of the non-trivial metric. This chapter considers two such defects in ³He-A, the domain wall, and disclination line. In general relativity, these defects correspond respectively to planar and linear singularities in the field of vierbein, at which the metric is degenerate. The static domain wall is analogous to the surface of infinite red shift in general relativity. The quantum mechanical communication between the worlds on two sides of the wall is considered. Disclination gives rise to the effective conical space for quasiparticles, with curvature concentrated on the disclination. The effective space outside the disclination core is flat, but the proper length of the circumference of radius R around the axis depends on the type of disclination and can be smaller or larger than 2πR. In the latter case the disclination is analogous to the anti-gravitating cosmic string.