Meaning of the distance between galactic objects in GR

In summary, the distance between galactic objects in General Relativity (GR) is not simply a measure of space but is influenced by the curvature of spacetime caused by mass and energy. This curvature affects how distances are calculated, leading to phenomena such as gravitational lensing and the expansion of the universe. The concept of distance in GR incorporates both the geometric properties of spacetime and the effects of gravity, making it a more complex and dynamic measure than in classical physics.
  • #1
cianfa72
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TL;DR Summary
About the meaning of the distance between galactic objects in the Universe in the context of GR
Hi, I was thinking about the claim that for instance Sagittarius A* (Sgr A*) black hole is a at 26996±29 light years from the Earth from a GR point of view.

Assuming a FLRW model for the Universe, maybe the above meaning is that at a given cosmological time ##t## (the "present" time) the proper distance between the Earth and Sgr A* evaluated on the spacelike hypersurface of constant cosmological time ##t## is actually 26996±29 light year.

Does it make sense ?
 
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  • #2
The FLRW model is not a good model at the galactic scale as the galaxy is a gravitationally bound system. Instead, the spacetime on galactic level is pretty well described (apart from locally near extreme objects like black holes) by the weak field approximation. Sgr A* being some 27000 ly away is the corresponding distance in the galactic rest frame.
 
  • #3
Orodruin said:
Instead, the spacetime on galactic level is pretty well described (apart from locally near extreme objects like black holes) by the weak field approximation. Sgr A* being some 27000 ly away is the corresponding distance in the galactic rest frame.
Does the weak field approximation give rise to a metric tensor on spacetime as a manifold ?

Edit: is the galactic rest frame the spacetime coordinate chart in which on average the galaxy's constituents are "at rest" -- i.e. have timelike worldlines with constant spatial coordinates?
 
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  • #4
cianfa72 said:
Does the weak field approximation give rise to a metric tensor on spacetime as a manifold ?

Yes.


cianfa72 said:
Edit: is the galactic rest frame the spacetime coordinate chart in which on average the galaxy's constituents are "at rest" -- i.e. have timelike worldlines with constant spatial coordinates?
No. It is the irrotational frame where the galaxy com is at rest.
 
  • #5
Orodruin said:
No. It is the irrotational frame where the galaxy com is at rest.
Could you be more specific ? As far as I can understand, it is the coordinate chart in which the galaxy's COM (Center of Mass) is "at rest" -- i.e. its timelike worldline has constant spatial coordinates in that chart (only varying timelike coordinate time ##t##).

What does it mean it is an irrotational frame/coordinate chart ? Thanks.
 
  • #6
cianfa72 said:
What does it mean it is an irrotational frame/coordinate chart ?
Does not rotate with the galaxy.
 
  • #7
Orodruin said:
Does not rotate with the galaxy.
Sorry, I don't grasp the point. Do the galaxy's constituents rotate in that irrotational chart (i.e. their timelike worldlines parametrized by the coordinate time ##t## rotate in that chart) ?
 
  • #8
cianfa72 said:
Do the galaxy's constituents rotate in that irrotational chart
Yes, they move around in approximately circular orbits.
 
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  • #9
Orodruin said:
Yes, they move around in approximately circular orbits.
Ah ok, that means galaxy's constituents paths (parametrized by the coordinate time ##t##) as described in the irrotational chart move like circular orbits around the galaxy's COM.
 
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  • #10
Well, approximately circular. There are lots of local variations to that, but in general yes.
 

FAQ: Meaning of the distance between galactic objects in GR

What does the distance between galactic objects represent in General Relativity?

In General Relativity (GR), the distance between galactic objects is not merely a simple spatial measurement but is influenced by the curvature of spacetime caused by mass and energy. This means that the distance can vary depending on the gravitational field and the path taken through spacetime, making it a more complex concept than in classical physics.

How is the distance between galaxies measured in the context of GR?

The distance between galaxies in the context of General Relativity is often measured using redshift, which indicates how much the wavelength of light has stretched as the universe expands. Astronomers also use methods such as standard candles (e.g., Type Ia supernovae) and gravitational lensing to determine distances, accounting for the curvature of spacetime.

Does the expansion of the universe affect the distance between galactic objects?

Yes, the expansion of the universe, described by the Friedmann-Lemaître-Robertson-Walker (FLRW) metric in GR, affects the distance between galactic objects. As the universe expands, galaxies move away from each other, and this expansion alters the effective distance between them over time, which is observed as redshift in their light.

What is the significance of the cosmic scale factor in measuring distances in GR?

The cosmic scale factor is a crucial component in measuring distances in General Relativity as it describes how distances in the universe change over time due to cosmic expansion. It relates the present size of the universe to its size at a previous time, allowing astronomers to calculate proper distances between galaxies at different epochs.

How does gravitational lensing affect our understanding of distances between galaxies?

Gravitational lensing occurs when a massive object (like a galaxy or cluster of galaxies) bends the light from a more distant object. This phenomenon can create multiple images or distort the appearance of the background object, which helps astronomers measure distances more accurately. It provides insights into the distribution of mass in the lensing object and the geometry of spacetime, enhancing our understanding of distances in the universe.

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