Recent content by pseudoriemann

I've really posted in this thread about things and details which, according to my opinion, are wrong and I've really explained it. I didn't ever say "I can't get the answer", please check this thread if you want because that's wrong. Ok, this a too famous paper in physics and I recommend you...

If you impose this limit through the geodesic equation way it's ok, but what I'm questioning here is the Poisson equation in such a limit and the information neglected of the rest of EFE.

But if we consider the Schwarzschild solution, we just set the M parameter looking at ##r \rightarrow \infty##, using the weak field limit (so the EFE in such a limit implies the Poisson equation, thus we really have a source of gravity there); however, in the Schwarzschild solution, we really...

Thank you for the information. I didn't say 'personal alternative theory', but 'alternative theory'. For example I think that GR and Brans-Dicke theory are different theories of gravitation and there are lots of discussions in PF about Brans-Dicke theory and so on. Anyway, I didn't want to...

Yes, thank you Peter Donis, I'll try to post in this way if you prefer it. I'm considering only vacuum solutions, yes. Vacuum solutions only mean that the stress-energy tensor is zero but there may be a source of gravity in such a spacetime (for example, a M mass). According to my oppinion, the...

Finally, I would like to say that I'm working in an alternative theory which, among other things, it maybe improve this limit (in general, I'm a supporter of GR but I don't agree in 100% with this particular point of the theory and I think this limit could be improved by a better theory than...

I think ##\eta## is a backgroun metric, i. e. a Minkowski spacetime metric or de Sitter (Anti de Sitter) metric and, for example, if we consider a Minkowski spacetime background, then ##\partial\eta \neq 0## in spherical coordinates (you can check it, for example, in the following book: T. Ortín...

I know, I'm just considering the form I gave because in the general case if we only have a spacetime with a spherical mass then Birkhoff's theorem determines this form and that's what I'm considering. I don't know what you mean. If we neglect the terms which have ##h_{rr}## multiplying the...

Thank you for the posts, I'll try to answer quickly because I don't really have too much time before Monday to post, but I'm going to try...

This weekend I can't post anything so I will see you on Monday, thank you so much !

Thank you for the link. I think the expression (23) is wrong, because for a spherically symmetric spacetime with the typical coordinates {t, r, theta, phi} we have ##\partial_{\lambda}\eta_{\mu \nu} (x) \neq 0 ## and the link says that the line element of such a limit is (33) but for the above...

The above derivation is mine and I think that the weak field limit is equivalent to consider low velocities and curvature, setting ##c = constant##, in fact the value of ##c = 3 \times 10^8 m s^{-1}## doesn't appear in GR, we know this value because of experiments with light (whose mass is zero)...

But ##c## is only a constant, you can take ##c^{2}G_{rr}## and then this factor and ##G_{tt}## are of the same order in ##c##, why do we neglect the Einstein equation ##c^2G_{rr}=c^2kT_{rr}##? In fact, in Planck units we can take ##c=1## and ## O(v^2) \rightarrow 0 ## so there wouldn't be any...

ok let's do it (I apologize in advance about possible mistakes): For example, if we considered a static spherically symmetric spacetime in a coordinate system where ##ds^2 = g_{t t} (r)c^2dt^2-\frac{dr^2}{g_{tt}(r)}-r^2d\Omega^{2}## then we have ##R_{\theta...

Thank you Markus Hanke, in this limit Tr r is neglected but what I'm saying is that according to my opinión Gr r is not neglected and the same for Gθ θ and Gφ φ, so the Einstein equations are not totally valid in this limit. You may write the expressions of these components of the Einstein...