Light deflection and time delay in the gravitational field of a spinning mass

Abstract

In this paper we consider the possibility of measuring the corrections induced by the square of the parameter a_g of the Kerr metric to the general relativistic deflection of electromagnetic waves and time delay in an Earth based experiment. It turns out that, while at astronomical scale the well known gravitoelectric effects are far larger than the gravitomagnetic ones, at laboratory scale the situation is reversed: the gravitomagnetic effects exceed definitely the gravitoelectric ones which are totally negligible. By using a small rapidly rotating sphere as gravitating source on the Earth the deflection of a grazing light ray amounts to 10^{-13} rad and the time delay is proportional to 10^{-23} s. These figures are determined by the upper limit in the attainable values of a_g due to the need of preventing the body from exploding under the action of the centrifugal forces. Possible criticisms to the use of the Kerr metric at a_g^2 level are discussed.