Riemann's Acceleration in Light of the Howusu Metric Tensor in Spherical Polar Coordinates and Its Effect on the Theory of Gravitation

Abstract

This work explores the ramifications of introducing the Howusu Metric Tensor into the theoretical framework of Riemann's Acceleration within spherical polar coordinates, aiming to deepen our comprehension of gravitational interactions. Bridging the gap between traditional Cartesian coordinates and spherical polar coordinates, the research navigates the challenges posed by rotational symmetry to seamlessly integrate Riemann's Acceleration into the latter. The Howusu Metric Tensor emerges as a novel mathematical construct tailored to the intricacies of spherical polar coordinates, enabling a refined representation of spacetime curvature. The Results which are Riemann's acceleration in light of the Howusu metric tensor in spherical polar coordinates and consequently a generalization of the Newton's equations of motion showcase the modified Riemann's Acceleration equations in spherical polar coordinates, revealing subtle differences when compared to conventional Cartesian coordinates. Comparative analyses underscore the impact of the Howusu Metric Tensor, both quantitatively and qualitatively, offering insights into the altered dynamics of gravitational forces. This signifies a paradigm shift in our approach to gravitational theory, showcasing the potential of the Howusu Metric Tensor to unravel novel insights and broaden the horizons of theoretical physics. The findings not only advance our understanding of gravitational interactions but also set the stage for further exploration and refinement in the ever-evolving landscape of theoretical physics.