Hm, ok. I understand this. But the question is: if the energy-momentum-tensor is increased, what happens with the volume?
From the standard form of a static, spherically symetric metric.
## ds^2 = B(r)c^2dt^2 -A(r)dr^2 - r^2(d\theta^2+sin^2 \theta d\phi^2) ##
so
## (g_{\mu\nu}) = diag (B(r)...
Yes, I see. But how do we know that it doesn't become "the opposite of minkowski" as it approaches infinity?
While deriving a metric from the standard form
##ds^2 = B(r)c^2dt^2 - A(r)dr^2 -r^2(d\theta^2 + sin^2\theta d\phi^2)##
It's always assumed that B(r) and A(r) approach to 1. I know...
I fully agree for the asymptotical flatness of the solar system. It's measured with high precision.
But why do we assume the galaxy asymptotically flat?
Because flatness means "no influence of gravity" if we assume that gravity is the same as curvature of spacetime. I understand that.
But...
ok, they write, that a volume of a small ball of testparticles will decrease in time. And that's the basic meaning of "gravity attracts".
My question is another: If I the mass is increased, will the volume increase or decrease because of the additional mass?
... can the metric tensor help...
Could it be not true on galaxy level? It is true in the solar system and on earth, but on galaxy level we cannot fit the rotation curves with this assumption. Could it be possible that the assumption "when r goes to infinity, then spacetime becomes minkowski" is violated for galaxies?
If that...
In derivation of the standard form of a spherical symmetric metric, always the assumption is made: minkowski spacetime is in the infinity. Why is this done? Could it be violated/not true? For example on the galaxy scale?
Ah, ok, that you mean: the real tides (of the oceans). But those are triggered by the moon moving around the Earth and the moon takes 12 hours for one cycle.
Thank you for the answer! Ah, free fall condition. I understand this. But, after understanding that it's free fall, why is it only negligible "to first approximation"?
Is there tidal gravity left knowing that the Earth (and me) is in free fall? What is tidal gravity? Why does is act contrary to...
During the day, I am between sun and earth. During the night, I am behind the Earth if I'm looking from the sun.
So its
Day: sun-me-earth
night: sun-earth-me
So the forces of gravity from sun and Earth add during the night, but during the day, the sun attracts me away from the earth...
In this article:
https://link.springer.com/article/10.1140/epjc/s10052-017-4695-y
they explain that introducing new fields to the EFE and introducing unknown particles is equivalent. Therefore, modifying GR is not an alternative to dark matter, its conceptually the same.
Newton perfectly fits for the solar system, but not for whole galaxies. Of course it can be dark matter. But to gain alternative approaches, one could ask: What is the difference between the solar system and the whole galaxy? One big difference I find is that the solar system surrounds the...