Gravitational Metric Tensor Exterior to Rotating Homogeneous Spherical Masses

Abstract

The covariant and contravariant metric tensors exterior to a homogeneous spherical body rotating uniformly about a common φ axis with constant angular velocity ω is constructed. The constructed metric tensors in this gravitational field have seven non-zero distinct components.The Lagrangian for this gravitational field is constructed. It is used to derive Einstein’s planetary equation of motion and photon equation of motion in the vicinity of the rotating homogeneous spherical mass.

Journal of the Nigerian Association of Mathematical Physics, Volume 19 (November, 2011), pp 49 – 54