Comments about "Geodesics in general relativity" in Wikipedia

This document contains comments about the article Geodesics in general relativity in Wikipedia

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In the last paragraph I explain my own opinion.

Contents

• 1. Mathematical expression
• 2. Equivalent mathematical expression using coordinate time as parameter
• 3. Derivation directly from the equivalence principle
• 4. Deriving the geodesic equation via an action
• 5. Equation of motion may follow from the field equations for empty space
• 6. Extension to the case of a charged particle
• 7. Geodesics as curves of stationary interval
• 8. Derivation using autoparallel transport
• 9. See also

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Introduction

The article starts with the following sentence.

Importantly, the world line of a particle free from all external, non-gravitational forces is a particular type of geodesic.

That is one of the most simple examples?

In general relativity, gravity can be regarded as not a force but a consequence of a curved spacetime geometry where the source of curvature is the stress–energy tensor (representing matter, for instance).

My understanding is that matter can be described by a stress-energy tensor which physical means that the path of an object follows a geodesic in spacetime.

Thus, for example, the path of a planet orbiting a star is the projection of a geodesic of the curved four-dimensional (4-D) spacetime geometry around the star onto three-dimensional (3-D) space.

My understanding is that I would change space into: space and time.

1. Mathematical expression

The quantity on the left-hand-side of this equation is the acceleration of a particle, so this equation is analogous to Newton's laws of motion, which likewise provide formulae for the acceleration of a particle.

My understanding is that a particle can also be a planet or a star considered as a point mass.

2. Equivalent mathematical expression using coordinate time as parameter

3. Derivation directly from the equivalence principle

4. Deriving the geodesic equation via an action

5. Equation of motion may follow from the field equations for empty space

6. Extension to the case of a charged particle

7. Geodesics as curves of stationary interval

8. Derivation using autoparallel transport

9. See also

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