Gauge Gravitation Theory And The Detection Of The Gravitomagnetic Field

We always need to deal with the momentum and angular momentum of asingle elementary particle or quantum felds in curved spacetime. Regarding tothe local momentum and angular momentum operators, as well as local covari-ant momentum and angular momentum operators, we study their commutationrelations and SO(3,1) gauge transformation properties, respectively. A local de-composition method of the gravitational feld is introduced. In this way, a newset of momentum and angular momentum operators which satisfy both SO(3,1)gauge-invariance and some self-consistent tetrad commutation relations are pro-posed.The rotation of the Earth produces gravitomagnetic components of the Rie-mann curvature tensor, which are of the order of1010of the Newtonian termsarising from the mass of the Earth. Detection of the gravitomagnetic feld is veryimportant, since in addition to testing one of the most fundamental predictions ofgeneral relativity, it is the most feasible way to test Mach’s Principle in the innersolar system. We review the experimental scheme for detecting the gravitomag-netic efect with an orbiting gravity gradiometer in an inertial frame. Two factorswhich can afect the experiment, satellite positioning errors and Earth’s multipolemoments, are analyzed. We derive the satellite positioning accuracy required forconstruction of matched templates with sufcient precision. We fnd that thesatellite orbit must be carefully selected to avoid some dangerous altitudes atwhich Earth’s multipole moments can mask gravitomagnetic signals. Allowableorbit altitudes are computed. We also examine an alternative scheme, in whichthe gradiometer is fxed to a local inertial frame defned by gyroscopes. In this ex-periment, the gradient signal grows linearly with time due to the Lense-Thirringefect, and the satellite positioning errors and Earth’s multipole moments becomenegligible.