geodesic motion

The primary objective is to measure deviations from geodesic motion.

Results for the symmetries of equations and equivalent Lagrangians are applied to the problem of geodesic motion in Riemannian space–times.

A particle executing geodesic motion has zero value for each component of the acceleration four vector.This conforms to the fact that Gravity is not a force.

In them, he showed that if elementary particles were treated as singularities in spacetime, it was unnecessary to postulate geodesic motion as part of general relativity.

The metric tensor in general relativity is an essential object, since proper time, arc length, geodesic motion in curved spacetime, and other things, all depend on the metric.

In general relativity, the principle of inertia is replaced with the principle of geodesic motion, whereby objects move in a way dictated by the curvature of spacetime.

It describes the geodesic motion of a free particle on the non-compact Riemann surface where is the upper half-plane endowed with the Poincaré metric and is the modular group.

The concept of geodesics becomes central in general relativity, since geodesic motion may be thought of as "pure motion" (inertial motion) in spacetime, that is, free from any external influences.

This approach can be extended to fields rather than a system of particles (see below), and underlies the path integral formulation of quantum mechanics, and is used for calculating geodesic motion in general relativity.

This new class of preferred motions, too, defines a geometry of space and time-in mathematical terms, it is the geodesic motion associated with a specific connection which depends on the gradient of the gravitational potential.

For instance, in the general theory of relativity, acceleration is not an effect (since it is not a generally relativistic vector); the general relativistic effects comparable to those of Newtonian mechanics are the deviations from geodesic motion in curved spacetime.

Physically, these describe different universes in which all the same events and interactions are still (causally) possible, but a new additional force is necessary to effect this (that is, replication of all the same trajectories would necessitate departures from geodesic motion because the metric is different).

This theory is based on principles like the equivalence principle, the general principle of relativity, the principle of general covariance, geodesic motion, local Lorentz covariance (the laws of special relativity apply locally for all inertial observers), and that spacetime curvature is created by stress-energy within the spacetime.