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So I just finished off learning quantum mechanics and special relativity. I just realized that in general relativity, there is Einstein field equation which must be solved in order to talk about physical movements.

But I see several solutions. So is there a thing as a solution that describes our universe perfectly at astronomical scales/macroscopic level (not quantum level)?

Or do we have to solve the equation for different cases occurring in our reality?

Qmechanic
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user42935
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1 Answers1

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The situation is not at all different from that in Newtonian physics. If you have Newton's law for gravity, i.e. $$ \vec F = -\frac{G m_1 m_2}{\vert\vec x_1 - \vec x_2\vert^3} (\vec x_1 - \vec x_2) $$ in order to exactly describe any motion, in principle you need to know some initial configuration in which you know the exact position of any object in any galaxy. But in practical calculations it is enough to know the state of some subsystem which interacts only weakly with the rest. Like, for example, just consider the motion of one planet around the sun. Or more accurately the motion of all planets in the solar system, but ignoring other stars in the galaxy.

The situation is exactly the same in GR. You cannot measure all positions of each object (and if you could the equations would be far to complicated to ever be solved), but you can consider subsystems.

Common solutions are for example the Schwarzschild solution for a spherical object, or the Friedmann–Lemaître–Robertson–Walker solution, which models cosmology.

André
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    I would say that it is not quite exactly the same -- in principle, we can work out the exact force for an arbitrarily complex Newtonian system. In full GR, it might not be possible to produce an exact solution that corresponds to an arbitrary mass distribution. – Zo the Relativist Mar 20 '14 at 15:24
  • Yes, but we are not talking about an arbitrary mass distribution here but the mass distribution of the universe as we find it. I would say, this mass distribution has to correspond to some exact solution of GR, otherwise something with GR would be wrong. – André Mar 20 '14 at 16:52
  • Not necessarily:

    1. It is not necessary that the mass distrubtion of the universe is resolveable to an analytic solution of GR. This is in fact unlikely, considering that the Einstein equation exhibits chaos theory.

    2. Even if it were not resolveable to an exact solution, known exact solutions have been shown to be extremely relevant to astrophysics in their relevant realms of applicability.

    3. Post newtonian expansions have shown that GR is by far the best choice for describing known gravitational phenomena.

     – Zo the Relativist Mar 20 '14 at 17:13