A Study of Geodesic Equation From Variational Principle

Abstract

This paper employs variational principle in studying geodesic Eqⁿ. In mathematical studies, a variational principle enables a problem to be solved employing calculus of variations that concerns seeking functions that increase the values of quantities that rely on those functions. For instance, the problem of ascertaining the shape of a hanging chain suspended at both ends can be solved using variational calculus. Hence, the variational principle is a function that lessens the gravitational potential energy of the chain. Geodesic Eqⁿ is a procedure used in mathematics, specifically in Riemannian geometry that results in obtaining geodesics. Actually, these represent the paths of particles with no proper acceleration, their motion pleasing the geodesic equations. As the particles are subject to no appropriate acceleration, the geodesics generally signify the straightest path between two points in a bent spacetime. The article has investigated into the relation between the variation principle and geodesic equations that are particularly used in general relativity in physics as well.