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...

I'm having trouble reproducing some of the results regarding gravitational waves in the Wald's General Relativity In section 4.4 of gravitational radiation, eq.4.4.49 shows the far-field generated by a variable mass quadrupole: $$ \gamma_{i j}(t,r)=\frac{2}{3R} \frac{d^2 q_{i j}}{dt^2}...

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 &...