Register to reply 
Are Solutions to GR Field Equations Chaotic? 
Share this thread: 
#1
Jul614, 07:41 AM

P: 11

The field equations of general relativity are nonlinear. 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 socalled attractors constrain the system within defined regions of state space. These attractors in state space can be points, loops (periodic), or "strange" (nonperiodic). I'm thinking that when a star undergoes gravitational collapse, it might not evolve into a classic, orderly, steadystate 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? 


#2
Jul614, 10:43 AM

Homework
Sci Advisor
HW Helper
Thanks
P: 12,870

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



#3
Jul614, 12:23 PM

P: 11




#4
Jul614, 10:16 PM

Homework
Sci Advisor
HW Helper
Thanks
P: 12,870

Are Solutions to GR Field Equations Chaotic?
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. 


Register to reply 
Related Discussions  
Solutions to equations of motion for free scalar field  Advanced Physics Homework  0  
Solutions to Field Equations with Einstein Tensor = 1  Special & General Relativity  3  
Solutions of the nonlinear Field Equations  Special & General Relativity  38  
Looking for Best References with OfftheShelf Exact Solutions to Einstein's Field Equations for Charged Perfect Fluids  General Physics  0  
Exact solutions of Einstein's field equations  General Physics  6 