# Are Solutions to GR Field Equations Chaotic?

1. Jul 6, 2014

### Juan Largo

The field equations of general relativity are non-linear. There are exact analytic solutions to the equations for special symmetrical cases, e.g. Schwarzschild's solution for a black hole. But in general, wouldn't there be other chaotic solutions as well?

A chaotic system is analytically unpredictable; however, one or more so-called attractors constrain the system within defined regions of state space. These attractors in state space can be points, loops (periodic), or "strange" (non-periodic). I'm thinking that when a star undergoes gravitational collapse, it might not evolve into a classic, orderly, steady-state Schwarzschild black hole at all, but a chaotic system instead. And depending on the initial conditions of that star prior to the collapse, it could end up in any number of different chaotic states, depending on which attractor it encountered along the way.

Have there been attempts to solve the GR field equations either numerically or using analog computers, specifically for collapsing stars? Is there any literature on this subject?

Last edited: Jul 6, 2014
2. Jul 6, 2014

### Simon Bridge

Even Newtonian gravity has chaotic solutions so you'd expect GR to have them too.

3. Jul 6, 2014

### Juan Largo

True, which is why the 3-body problem is analytically "unsolvable." But my real question is whether a real star would ever actually collapse into a classical Schwarzschild black hole, or become something else entirely.

4. Jul 6, 2014

### Simon Bridge

The answer is no and yes.
It would be very surprising for a real star to collapse into a classical SBH as you say, since that model has a bunch of simplifications to it. However, we would expect the final object to be some form of black hole.

Notice that Newtonian gravity has predictable outcomes despite its chaotic nature - GR is the same.
You'd get black holes for the same reason you'd get big balls of gas. You won't get a BH exactly conforming to a simplified solution the same way that stars are not perfect spheres.