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Jan
16
accepted Einstein tensor of a gravitational source
Jan
15
answered Einstein tensor of a gravitational source
Jan
13
revised Einstein tensor of a gravitational source
added 293 characters in body
Jan
12
revised Einstein tensor of a gravitational source
deleted 1 character in body
Jan
12
asked Einstein tensor of a gravitational source
Jan
12
accepted Simple quadrupole field not yet in Lorenz gauge?
Dec
29
comment Simple quadrupole field not yet in Lorenz gauge?
I am quoting 1st paragraph page 80, "in the case of linearized gravity, we can use the restricted gauge freedom, equation (4.4.27), to achieve the radiation gauge $\gamma=0$, $\gamma_{\mu 0}=0$ for $\mu=1,2,3$ in a source free region"
Dec
29
accepted Proving that Killing form contractions with geodesics are constants of motion
Dec
29
comment Proving that Killing form contractions with geodesics are constants of motion
ok that makes sense
Dec
29
comment Proving that Killing form contractions with geodesics are constants of motion
How do you evaluate the expression $\partial_{;\nu} \frac{dP^\mu}{d\lambda}$? (or $\nabla_{\nu} \frac{dP^\mu}{d\lambda}$ in your previous notation)
Dec
29
revised Proving that Killing form contractions with geodesics are constants of motion
edited body
Dec
29
revised Proving that Killing form contractions with geodesics are constants of motion
deleted 91 characters in body
Dec
29
revised Proving that Killing form contractions with geodesics are constants of motion
added 2 characters in body
Dec
29
comment Proving that Killing form contractions with geodesics are constants of motion
@MBN, no, you are missing the $\frac{d^2 P^{\mu}}{d \lambda^2} \xi_{\mu}$ term
Dec
29
comment Proving that Killing form contractions with geodesics are constants of motion
3) $\partial_{;\nu} \frac{d P^{\mu}}{d\lambda}$ is not meaningful since $P^{\mu}$ is not a function of coordinates but of $\lambda$, so there is no point in complicating things here; $\frac{d}{d\lambda}( \frac{d P^{\mu}}{d \lambda})$ is just $\frac{d^2 P^{\mu}}{d \lambda^2}$
Dec
29
comment Proving that Killing form contractions with geodesics are constants of motion
2) What is the point of using two notations for the covariant derivative? $\nabla_{\mu}=\partial_{;\mu}$
Dec
29
comment Proving that Killing form contractions with geodesics are constants of motion
A few observations: 1) your expression has the index $\mu$ repeated four times, which might be confusing
Dec
29
comment Proving that Killing form contractions with geodesics are constants of motion
@Qmechanic, the reason to call it a form is that symmetrization of indices with the covariant index of a derivative ought to be a covariant index as well. But I agree that it might lead to confusion with the other Killing form used in Lie algebras
Dec
29
asked Proving that Killing form contractions with geodesics are constants of motion
Dec
28
comment Simple quadrupole field not yet in Lorenz gauge?
why would the $\gamma_{00}$ component affect the values of $\partial_{i} \gamma_{i1}$ and $\partial_{i} \gamma_{i2}$? Also, As far as I can see, $\gamma_{\mu 0}$ is zero for $\mu=1,2,3$