Cosmic String Topological Defect

Metric (z-axis string):
ds² = −dt² + dr²
+ (1−4Gμ)²r²dφ² + dz²

Deficit angle: δ = 8πGμ
Topology: cone, not plane

Lensing: twin images
Δθ = 8πGμ·D_LS/D_S

Phase transition → π₁(G/H)≅ℤ
(fundamental group nontrivial)
Kibble mechanism 1976 · cosmic strings · topological defects · conical geometry · gravitational lensing