An example of induced centrifugal force in general relativity

Abstract

Thirring's solution1 for a rotating spherical mass is cited often as an example which exhibits induced Coriolis and centrifugal forces in general relativity. Previously, it was pointed out that the 'centrifugal terms' proportional to the square of the angular velocity actually represented quadrupole effects. These effects arose as a consequence of the latitude-dependent velocity distribution which generated an axially symmetric (non-spherical) mass distribution. This raises the question: Are there solutions to Einstein's equations which exhibit induced centrifugal force? If no such solutions exist, then the concept of induced rotation of inertial frames breaks down. Such a lack of connection between rotating masses and induced inertial frame rotation would in turn imply a breakdown of the Machian idea that an inertial frame is a system of reference in which the stress-energy of the universe is at rest on the average. Here we demonstrate that there are solutions to Einstein's equations which exhibit induced centrifugal force (other solutions may also be of interest in this connection).