Hi George,
you are perfectly right, my question does not makes sense without specifying the observer's motion with respect to the photon. So I guess the correct answer is Ich's:
f=-u_a k^a=-g_{ab}u^bk^a ,
because it takes into account that. However, I am curious about the quantity...
Hi Ich,
thank you for your answer.
This is the point: I would like to know what is the energy of the photon in a generic system of coordinates in which the metric is described by g_{\mu\nu} . Is it g_{ij}P^iP^j? (sum is over spacial indexes)
Is the implicit summation over 0,1,2,3 or...
Hi atyy,
thank you for your answer!
The link seems very interesting. However, I was hoping you could point some intuitive physical argument, not a mathematical one.
Cheers,
G.
Hi everybody!
I am wondering, among other things, whether the Special Relativity relationship E = p for a photon (I am using c = 1 units ) is still valid in General Relativity.
Let me explain my question in detail. By applying the null geodesic condition with a diagonal metric, we obtain...
Hi Everybody!
I am raising this post from the dead just to list a few algorithm I used with success to integrate the above function:
1) Andrew Hamilton's FFTLog algorithm from http://casa.colorado.edu/~ajsh/FFTLog/. It permits you to integrate not only f(x)*sin(x) but any integrand in the...
Hi mathman, thank you for your answer. You are right indeed.
I tried to expand the sine & cosine as my first approach, but I made a stupid mistake in the calculation of the coefficients and I got wrong results. I re-did everything and now I get results as precise as 10^-6. Thank you...
I forgot to mention that I need to compute the functions for a very large array of "r" values from within a C++ program. Thus, pasting the result from Mathematica is not helpful :)
Cheers,
Guido
Hi everybody!
I kindly request your help. I have to compute functions like
\frac{ \sin (r x) - r x \cos (r x)}{r^3}
(primitive function of x sin(rx) )
or
\frac{ -r x (120 - 20 r^2 x^2 + r^4 x^4) cos(r x) +
5 (24 - 12 r^2 x^2 + r^4 x^4) \sin(r x)}{r^7}
(primitive function of x^5 sin(rx) )...
uart, thank you very much for the idea! This way I can evaluate the integral almost analytically.
I am trying a slightly modified version of your approach by using a Splines interpolation of f(k) instead of a linear one; I will let you know the outcome. By the way, do you have any idea on how...
Hi,
did I omit some important information? Or maybe I posted in the wrong forum?
By the way, I found a routine in the GNU Scientific Library called "QAWF adaptive integration for Fourier integrals" that could be what I am looking for. I only need to get acquainted with GSL, and it is going...
Hi everybody!
I kindly request your help in optimizing the numerical integration of the following expression:
\xi (r)=\frac{1}{2\pi ^2}\int_{-\infty}^{\infty}f(k)\cdot \sin(k\cdot r)\cdot dk
f(k) vanishes outside the boundaries k=0 and k=2; I have got k and f(k) as float arrays, so we...
Hello everybody!
I was wondering if something like NRC Rankings exist also for European Grad Programs. In particular, I would really like to find a ranking (or merely a list) of the best Astronomy-Cosmology Grad Programs in UK-France-Spain-Italy-Portugal.
By the way, I suggest...
I found your assertion
an eye opener, so I tried to deduce it using the Heisenberg Uncertainty Principle.
Correct me if I'm wrong!
Let's think of the particle-particle collision in terms of the collision parameter b (the minimum distance the two protons would be in a collision if the...