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?
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.
