Physics — General Relativity · gravitomagnetism-lense-thirring
Problem
Consider a thin spherical shell of matter, with mass M and radius R, slowly rotating with an angular velocity Ω.
(a) Show that the gravito-electric field G vanishes, and calculate the gravito-magnetic field H in terms of M, R, and Ω.
(b) The nonzero gravito-magnetic field caused by the shell leads to dragging of inertial frames, known as the Lense--Thirring effect. Calculate the rotation (relative to the inertial frame defined by the background Minkowski metric) of a freely-falling observer sitting at the center of the shell. In other words, calculate the precession of the spatial components of a parallel-transported vector located at the center.