Einstein-Cartan theory keeps the metric-compatibility condition but allows the…
PHYSICS · Multi-part · Fermi University Physics · Relativity & Gravitation · Schwarzschild spacetime and the tests of general relativity · Schwarzschild spacetime and the tests of general relativity
The Geometry of Gravity, Ch Solar-system tests, the PPN framework and alternative theories
Problem
Einstein-Cartan theory keeps the metric-compatibility condition ∇αgμν=0 but allows the connection's antisymmetric part, the torsion, to be non-zero; torsion is sourced algebraically by the intrinsic spin density of matter and vanishes identically outside matter.
((a)) Name the assumption made when the Levi-Civita connection was fixed that Einstein-Cartan theory drops.
((b)) A future mission proposes to track a gyroscope in orbit around a rapidly rotating neutron star, entirely outside the star's surface, measuring its frame-dragging precession to a fractional precision of 10−6, far tighter than any solar-system test. The star's high spin might be expected to enhance any torsion effect. Decide whether, however precise, this vacuum-region measurement can discriminate Einstein-Cartan theory from general relativity, and justify the answer using where torsion is sourced.