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user 407460
Applies to questions of primarily educational value - not only questions that arise from actual homework assignments, but any question where it is preferable to guide the asker to the answer rather than giving it away outright. Please READ THE GUIDANCE IN META before asking homework-like questions.
2
votes
Derivative of line element in general relativity is zero?
Actually you don't need $\frac{d}{d\lambda} \sqrt{-g_{\mu\nu}\dot{x}^\mu \dot{x}^\nu} =0$.
Since $$L=\sqrt{-g_{\mu\nu}\dot{x}^ \mu \dot {x}^\nu} $$, $L^2$ also satisfies Euler-Lagrange equations.
So …
- 31
0
votes
How to prove $ g^{\mu\nu}\Lambda^{\rho}{}_{\mu}\Lambda^{\sigma}{}_{\nu}=g^{\rho\sigma} $ for...
Let me use condition
$${\Lambda^{-1}}^{\rho}_{}{\nu}= \Lambda_{\nu}{}^{\rho}$$
We can raise $\nu$ index left side as well as right side,
$${\Lambda^{-1}}^{\rho\nu}= \Lambda^{\nu\rho}$$
Now contract ab …
- 31