THE PARALLELISM BETWEEN THE HOWOSU RICCI SCALAR AND THE SCHWARZSCHILD RICCI SCALAR

Abstract

In this paper, new Ricci scalar using the Howusu metric tensor was derived which is valid for a gravitational field that is regular and continuous everywhere including all boundaries, continuous normal derivative everywhere including all boundaries, and its reciprocal decreases at infinite distance from the source. The results were compared with the well-known Schwarzschild Ricci Scalar using radial distance as the measuring index and it was discovered that, unlike the Schwarzschild Ricci Scalar, the Howusu metric tensor has a non-zero Ricci scalar as r tends to zero. Comparing also the Howusu Ricci Scalar R with the Schwarzschild Ricci Scalar R, it was found in this paper that, as ,  and as  , R tends to zero, and for the Schwarzschild Metric Tensor, the Ricci Scalar R is .  This Ricci scalar is a scalar quantity used to identify and make concrete the notion of curvature for all gravitational fields in nature