# Linked Questions

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### Lagrangian, metric and geodesics: obtention of equation of motion in GR [duplicate]

I would like to check my global understanding on G.R: how we determine the trajectories of particles. Everything starts from the equations of Einstein. We have to find a metric that satisfies ...
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### Geodesic equation from Euler - Lagrange

There are several ways to derive the geodesic equation. One of which is the variational method which I seemed to understand it because it was written in great details. Then it was mentioned that the ...
2answers
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### Geodesics equations via variational principle

I would like to recover the (timelike) geodesics equations via the variational principle of the following action: $$\mathcal{S}[x] = -m \int d\tau = -m \int \sqrt{-g_{\mu\nu}\,dx^{\mu}\,dx^{\nu}}$$ ...
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### Euler-Lagrange equation in General Relativity

In Relativity the Lagrangian of a free particle is \begin{align} \mathcal L=\sqrt{g_{ab}\frac{dx^a}{d\tau}\frac{dx^b}{d\tau}}\end{align} Since $\mathcal L$ is parameterization invariant we can always ...

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