# How come equations don't account for

#### schlynn

How come equations don't account for....

How come equations that involve the curvature of space don't include the fact that space is expanding. I mean, if its expanding near the speed of light, it seems like it would have some effect.

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#### Dale

Mentor
Re: How come equations don't account for....

I think there may be some misunderstanding, the http://en.wikipedia.org/wiki/Friedmann-Lema%C3%AEtre-Robertson-Walker_metric" [Broken] does account for it.

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#### schlynn

Re: How come equations don't account for....

Isn't that equations purpose to describe the expanding universe though? Are there any other equations that take account of the expanding of space?

#### ZikZak

Re: How come equations don't account for....

You are now asking: "Are there any equations that don't describe the expanding universe that describe the expanding universe?"

Perhaps you need to rephrase and make it clear exactly what you are attempting to ask for.

#### JesseM

Re: How come equations don't account for....

Isn't that equations purpose to describe the expanding universe though? Are there any other equations that take account of the expanding of space?
There's a general set of equations that tell you how spacetime curves in response to any possible distribution of matter and energy. For the particular distribution of matter and energy in the FLRW metric (and other similar metrics), the curvature of spacetime will be such that you get "expanding space".

#### Fredrik

Staff Emeritus
Gold Member
Re: How come equations don't account for....

The solutions of Einstein's equation that you can find in GR books all deal with highly idealized situations. Examples: The FLRW solutions are what you get when you assume that spacetime can be sliced into a one-parameter family of spacelike hypersurfaces that are all homogeneous and isotropic. (We can think of as them as representing space at different times). There are three such solutions. All of them describe an expanding universe. The Schwarzschild solution is what you get when you assume that spacetime is completely empty except for a spherical, non-rotating distribution of mass that has existed forever, and will continue to exist forever. There is only one such solution. The universe it describes isn't expanding.

If we're trying to describe spacetime near a star, it's pointless to use anything but the Schwarzschild solution. Spacetime can't be exactly Schwarzschild of course, since there are other things in the universe, but it's going to be a lot more like Schwarzshild than like FLRW for example, since space isn't at all homogeneous near the star. The universe is only homogeneous on very large scales.

So the correct solution describing spacetime near a star of finite life span in a universe where there are lots of other stars, distributed in galaxies and clusters of galaxies such that the large-scale structure is approximately homogeneous and isotropic, should almost certainly contain some amount of expansion, but it's likely to be ridiculously tiny. (Actually the expansion per year of a region the size of the solar system is very small in the FLRW solutions too. What I meant is that the expansion in the correct solution is likely to be ridiculously tiny compared to that).

I'm saying "likely" because I don't think these things have been proved conclusively yet.

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#### schlynn

Re: How come equations don't account for....

Thank you for the replys. I just saw some equations and realized they didn't account for it. But now I see the error, I can't make a conclusion like I did from just a few equations.

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