Dark Gravitational Field on Riemannian and Sasaki Spacetime

TL;DR

This paper develops a geometric framework incorporating dark matter into Riemannian and Sasaki spacetimes, deriving modified gravitational equations and exploring cosmological and tangent bundle applications.

Contribution

It introduces a novel geometric model of dark gravity within Riemannian and Sasaki spacetimes, extending classical equations to include dark matter effects.

Findings

Derived modified geodesic equations accounting for dark matter

Analyzed tidal forces and Einstein equations with dark gravity

Explored cosmological implications and tangent bundle extensions

Abstract

The aim of this paper is to provide the geometrical structure of a gravitational field that includes the addition of dark matter in the framework of a Riemannian and a Riemann--Sasaki spacetime. By means of the classical Riemannian geometric methods we arrive at modified geodesic equations, tidal forces, and Einstein and Raychaudhuri equations to account for extra dark gravity. We further examine an application of this approach in cosmology. Moreover, a possible extension of this model on the tangent bundle is studied in order to examine the behavior of dark matter in a unified geometric model of gravity with more degrees of freedom. Particular emphasis shall be laid on the problem of the geodesic motion under the influence of dark matter.