Effects of non-linearity of GR

[Orbb]

My question is to what extent the specifically non-linear properties of GR have been analyzed by theoretical physicists. Can they give rise to chaos and complexity, as many non-linear systems do?

I also wonder: I've so far mostly read about linearized descriptions of gravitational waves. However in fact, gravitational waves do not obey linear superposition. Has this been considered so far in any approach to quantum gravity (I especially refer to identifying gravitational waves with gravitons)? Because I think, that point is a fundamental difference to the fields contained so far in the standard model - correct me if I'm wrong with anything here. But maybe this second question would rather belong into the "Beyond the standard model" category.

I'm interested in your answers!

 

[Naty1]

Orbb,interesting questions!:

Systems that exhibit mathematical chaos are deterministic and thus orderly in some sense; this technical use of the word chaos is at odds with common parlance, which suggests complete disorder. A related field of physics called quantum chaos theory studies systems that follow the laws of quantum mechanics. Recently, another field, called relativistic chaos has emerged to describe systems that follow the laws of general relativity.

(note: there is no reference for "relativistic chaos"
but a brief write for quantum chaos:
http://en.wikipedia.org/wiki/Quantum_chaos)

http://en.wikipedia.org/wiki/Chaos_theory#Overview

If classical mechanics is a special case of quantum mechanics, there are likely quantum origins underlying classical chaos.

My guess is instabilities in relativity would be most likely near singularities.

 

[Dale]

My question is to what extent the specifically non-linear properties of GR have been analyzed by theoretical physicists. Can they give rise to chaos and complexity, as many non-linear systems do?

Even with Newtonian gravity a 3-body system can be chaotic.

 

[Orbb]

Even with Newtonian gravity a 3-body system can be chaotic.

I know. But I was wondering wether there are any complex/chaotic phenomena that especially arise due to the additional non-linearities of GR as compared to Newtonian gravity.

 

[Naty1]

But I was wondering wether there are any complex/chaotic phenomena that especially arise due to the additional non-linearities of GR as compared to Newtonian gravity.

Do you count the big bang and black hole singularities?? If so the answer is a resounding YES.

 

[Naty1]

I am rereading THE NATURE OF SPACE AND TIME a competing set of lectures by Penrose and Hawking and this comment caught my eye:

So it seems black holes really do have intrinsic gravitational entropy. ...This is related to the nontrivial topology of a black hole. The intrinsic entropy means that gravity introduces another level of unpredictability over and above the uncertainty usually assoicated with quantum theory.

Hawking, page 26
Not quite "chaos" but intriguing... his reasoning appears to be classical relativity based.
(This book is not for the casual reader.)

 

[Orbb]

I count any solution to the field equations ;) Thank you for your hint, i will try to take a look at these lectures. I already wonder if the holographic principle comes also into play here.

 

[AEM]

My question is to what extent the specifically non-linear properties of GR have been analyzed by theoretical physicists. Can they give rise to chaos and complexity, as many non-linear systems do?

I also wonder: I've so far mostly read about linearized descriptions of gravitational waves. However in fact, gravitational waves do not obey linear superposition. Has this been considered so far in any approach to quantum gravity (I especially refer to identifying gravitational waves with gravitons)? Because I think, that point is a fundamental difference to the fields contained so far in the standard model - correct me if I'm wrong with anything here. But maybe this second question would rather belong into the "Beyond the standard model" category.

I'm interested in your answers!

As I recall there was a small amount of work done on chaotic orbits in general relativity in the mid to late 1980s. I don't think that much came of it, however.

 

[AEM]

My question is to what extent the specifically non-linear properties of GR have been analyzed by theoretical physicists. Can they give rise to chaos and complexity, as many non-linear systems do?

I also wonder: I've so far mostly read about linearized descriptions of gravitational waves. However in fact, gravitational waves do not obey linear superposition. Has this been considered so far in any approach to quantum gravity (I especially refer to identifying gravitational waves with gravitons)? Because I think, that point is a fundamental difference to the fields contained so far in the standard model - correct me if I'm wrong with anything here. But maybe this second question would rather belong into the "Beyond the standard model" category.

I'm interested in your answers!

I should have done this BEFORE I made my previous post. Go to http://arxiv.org/find/gr-qc scroll down to "Experimental Search" and type in Chaos in General Relativity. You will find there's been some work done on the subject, more than I thought.