Geodesics

Following the formalism of Special and General Relativity in terms

of 4-vectors and metrics, a method is developed to derive the equations of motion

for test bodies.

This is achieved by applying the principle of least action for a certain path integral.

The case of Classical Mechanics using the Hamilton-Lagrange variational principle

is reviewed and a link is made with the separation of events in space-time.

The actual worldline followed by a test body is called a geodesic and it is that

worldline for which the separation is an extremum.

Via this approach a relativistic equivalent of the Lagrange equations is obtained

which leads to the geodesic equation, which allows the determination of

the actual worldline which will be followed by a test body.

Lecture Notes :

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