Ricci Tensor in General Ellipsoidal Geometry

Abstract

Abstract: The Ricci tensor has many applications in general relativity, topology, and theoretical physics [1]. Most planetary bodies have elliptical rather than spherical shapes. The Ricci tensor describes the change in the volume of the geodesic flows due to curvature and is related to gravitational tidal effects in general relativity. In this work, the Riemann and Ricci tensors are calculated in elliptical coordinates.

Keywords: Riemann, Ricci, Tensor, Ricci scalar, Elliptical coordinate.