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location United Kingdom
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visits member for 4 years, 1 month
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Studied physics and maths at school many years ago.


May
14
asked Carroll's derivation of the geodesic equations
May
14
accepted Why two different Lagrangians to derive geodesic equations?
May
13
comment Why two different Lagrangians to derive geodesic equations?
Any chance of a hint as to what that chain rule looks like? I cannot see how he substitutes (3.52) into (3.51) to get the equation at the bottom of page 69. Thank you for your patience.
May
13
comment Why two different Lagrangians to derive geodesic equations?
Thanks, but I just cannot see how he gets $d\tau$ as the denominator after making the affine parameter substitution (Equation 3.52).
May
13
comment Why two different Lagrangians to derive geodesic equations?
Thanks. I will try to derive the non-affine geodesic equations you give. In the meantime do you have a link to this derivation? I'm still puzzled as to how Moore starts with the square root Lagrangian and ends up with the affine geodesic equations.
May
13
comment Why two different Lagrangians to derive geodesic equations?
@Qmechanic - thanks. How come Valter Moretti's derivation here (which is over my head) starts with the square root Lagrangian and ends with (what I assume is) the affinely parametrized geodesic equations, ie my first equation?
May
12
asked Why two different Lagrangians to derive geodesic equations?
May
10
comment Differentiating the Lagrangian to find geodesic equations?
Yes, the Kronecker delta renames the index. I see it now. Thanks.
May
10
accepted Differentiating the Lagrangian to find geodesic equations?
May
10
asked Differentiating the Lagrangian to find geodesic equations?
Mar
4
accepted How to tell if a star is in a galaxy?
Mar
4
asked How to tell if a star is in a galaxy?
Dec
15
awarded  Popular Question
Dec
9
awarded  Popular Question
Nov
22
comment Derivation of the Riemann tensor confusion
After spending ages carefully typing it out in LyX, I couldn't resist showing it off here!
Nov
22
comment Derivation of the Riemann tensor confusion
I've just found this for the covariant derivative for a general tensor:$\nabla_{k}T_{j_{1}\ldots j_{s}}^{i_{1}\ldots i_{r}}=\partial_{k}T_{j_{1}\ldots j_{s}}^{i_{1}\ldots i_{r}}+\Gamma_{lk}^{i_{1}}T_{j_{1}\ldots j_{s}}^{li_{2}\ldots i_{r}}+\ldots+\Gamma_{lk}^{i_{r}}T_{j_{1}\ldots j_{s}}^{i_{1}\ldots i_{r-1}l}-\Gamma_{j_{1}k}^{l}T_{lj_{2}\ldots j_{s}}^{i_{1}\ldots i_{r}}\ldots-\Gamma_{j_{s}k}^{l}T_{j_{1}\ldots j_{s-1}l}^{i_{1}\ldots i_{r}}.$
Nov
22
comment Derivation of the Riemann tensor confusion
Carroll gives it on p58 here: arxiv.org/pdf/gr-qc/9712019.pdf. I notice that the upper index on the negative Gammas and the lower indices on the positive Gammas are constant, whilst the lower indices on the negative Gammas and the upper index on the positive Gammas are not.
Nov
22
accepted Derivation of the Riemann tensor confusion
Nov
21
comment Derivation of the Riemann tensor confusion
OK. It was that particular detailed equation for a general tensor I was interested in, but I'll take a look around.
Nov
21
comment Derivation of the Riemann tensor confusion
Thanks. Does $T^{d...a_{n}}$ mean $T^{da_{2}...a_{n}}$ etc? Do you have a reference for the derivation of this equation?