Recent content by CharlesJQuarra

Did you saw the quote of the approximation ##e^{I \omega | x' - x |}/| x' - x| \approx e^{I \omega R}/R##? This approximation assumes roughly that ##r_0 \ll R##, so we are already simplifying the dependence on the distance and ignore the size of the source. It would seem to me to be a much...

that is ##r_o## in the notebook, ##R## is the distance to the source, as it is explained in the snippet I quoted from Wald:

I would hope that to first order should be correct, in any case I'm not sure what you think it should be replaced with. After eq. 4.4.45, it makes a simplification where e^{I \omega | x' - x |}/|x'-x| becomes simplified to e^{I \omega R}/R. I'm not certain, but it seems to me that any error on...

The Einstein tensor (the geometric "marble") is proportional only to stress-energy tensor (the material "wood"). Einstein equations does not treat gravitational radiation on equal footing with matter or electromagnetic radiation

Here is the notebook content as a pdf

You should open it as a Mathematica notebook in order to see the structured code and the comments. Let me see if I can export it to a non-interactive text version

if you have Mathematica available, here is a notebook with the detailed calculation, with explanatory comments: https://github.com/CharlesJQuarra/GravitationCalcs/blob/master/GravWaveAnalysis.nb If someone wants to improve on it or propose changes, please, send me a pull request

In section 4.4 of gravitational radiation chapter in Wald's general relativity, eq.4.4.49 shows the far-field generated by a variable mass quadrupole: \gamma_{\mu \nu}(t,r)=\frac{2}{3R} \frac{d^2 q_{\mu \nu}}{dt^2} \bigg|_{t'=t-R/c} I have the following field from a rotating binary...

Hi Ben, True, I've should've added it explicitly. In any case the fact that the only nontrivial perturbation components are on the xx, xy, yx and yy means that derivatives of t and z do not show up in the gauge conditions \partial_{\mu} h^{\mu \nu} = 0. The issue is that, for example, I cannot...

I have a certain Ansatz for a gravitational wave perturbation of the metric h_{\mu \nu} that is nonzero near an axis of background flat Minkowski spacetime The Ansatz has the following form: g_{\mu \nu} = \eta_{\mu \nu} + h_{\mu \nu} = \begin{bmatrix} -1 & 0 & 0 & 0 \\ 0 &...