A Asymptotic Flatness: Minkowski Spacetime & Galaxy Scale

[Angelika10]

TL;DR

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?

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?

 

[PeroK]

Summary:: 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?

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?

It's a question of physical viability. What you're asking is why the gravitational effect of the Sun, for example, reduces with distance and eventually becomes negligible?

If it didn't, then the Earth would be significantly affected by the gravity of every star in the galaxy; plus every star in Andromeda.

There's no evidence for this. All the evidence points at the Sun having the only really significant effect.

In terms of asymptotic behaviour, the absolute mass is irrelevant.

 

[Orodruin]

What you're asking is why the gravitational effect of the Sun, for example, reduces with distance and eventually becomes negligible?

That is not entirely true. Even in the case of a spherically symmetric mass distribution in Newtonian gravity - you still have the option of an external field with zero divergence. This field is generally not considered to be part of the effect ”from the Sun”, but it does affect the boundary conditions.

The general idea however is that you want spacetime to be essentially Minkowski space far away from any sources or singularities.

 

[Angelika10]

It's a question of physical viability. What you're asking is why the gravitational effect of the Sun, for example, reduces with distance and eventually becomes negligible?

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?

If it didn't, then the Earth would be significantly affected by the gravity of every star in the galaxy; plus every star in Andromeda.

Because flatness means "no influence of gravity" if we assume that gravity is the same as curvature of spacetime. I understand that.

But, in analogy to electrodynamics: There is "no field" the asymptotic, not "flat field", as in general relativity. Why can't we assume this? Something like "vanishing spacetime" in the infinity?

 

[Angelika10]

The general idea however is that you want spacetime to be essentially Minkowski space far away from any sources or singularities.

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 that it's highly speculative, but could they divert from 1 in the infinity (B approching \infty, A approaching 0)?

 

[PeterDonis]

Why can't we assume this? Something like "vanishing spacetime" in the infinity?

This makes no sense.

I know that it's highly speculative

Yes, which means it's out of bounds for PF discussion, since we do not allow discussion of personal speculations. Instead of spending time speculating, you should be spending your time learning how the models used in astronomy and cosmology actually work and why they make the assumptions they do.

Thread closed.