All Questions
Tagged with non-linear-systems general-relativity
23 questions
14
votes
4
answers
2k
views
How do gravitational fields combine together in GR?
When we have 2 massive bodies coming close together say 2 black holes or 2 massive stars, how do their respective metrics/spacetime curvature combine in the space in between them?
Do we write
$$G_{\mu\...
- 2,042
1
vote
2
answers
161
views
Understanding linearity of Maxwell's equation compared to non-linarity of GR
In this post, it is mentioned that a linear equation means that the solutions 'do not interact with each other' or 'do not know' about each other. But we know that Maxwell's equations are linear ...
- 849
1
vote
2
answers
375
views
How to determine if gravity is roughly linear?
The Einstein field equations are famously nonlinear, which is one of the properties that makes them difficult to solve. I know (or at least I believe) that a linear system's behavior is roughly ...
- 3,347
3
votes
4
answers
649
views
Reformulate Einstein equations to make them linear
Is it possible to reformulate the Einstein equation in terms of a new variable, say $k_{\mu\nu}$ in terms of the metric $g_{\mu\nu}$, in order to make the Einstein equations linear in $k_{\mu\nu}$?
- 758
7
votes
1
answer
342
views
What evidence do we have for GR in the nonlinear regime?
The classical equations for Einstein's GR (modulo the cosmological constant) read
$$R_{\mu\nu} - \frac{1}{2} R g_{\mu\nu} = \kappa T_{\mu\nu}.$$ These equations have a complicated linearization that ...
- 820
7
votes
3
answers
4k
views
What do we mean when we say gravitational waves are non-linear and do not superpose like EM waves?
I have read this question:
Now it's not actually true that general relativity obeys a law of superposition, but it is an extremely good approximation for a small-amplitude gravitational wave passing ...
- 29.3k
10
votes
5
answers
3k
views
Addition of gravitational fields in general relativity
According to Newtonian gravity, when dealing with multiple sources of gravity, the net gravitational field equals the sum of the individual gravitational fields of each source.
Does the same hold for ...
- 613
-2
votes
3
answers
382
views
What is the evidence that gravitational fields don't sum up as a superposition?
Einstein's field equations are non-linear. Gravity gravitates (self-interacts). It's very complicated to solve Einstein's field equations for more than one central object. That are keystones in ...
- 255
-4
votes
1
answer
272
views
Self-coupling of gravity and gravitation escaping a black hole - contradiction?
The field equations are non-linear, that can be interpreted as gravity is coupling with itself, see for example here:
Non-linearity and self-coupling of gravity
I'm trying to understand what that ...
- 255
-1
votes
2
answers
211
views
Understanding EFE: RHS linear, LHS not?
Einstein's field equations are nonlinear. That means it is not allowed to add up the metric tensors. However, on the RHS of the field equations, there is only the stress-energy-momentum tensor, and it ...
- 255
3
votes
1
answer
409
views
Is this version of Einstein field equations linear?
While playing around with the Einstein field equations and trying to derive the Kerr metric, I came across the following derivation from Einstein's field equations:
$$R_{\mu\nu} = 8\pi \left(T_{\mu\nu}...
- 255
1
vote
0
answers
36
views
On the capacity for equations of motion to be contained in field equations
I've heard that the equation of geodesic motion can be derived from the vacuum Einstein field equations, although there appears to be some debate about how rigorously this can be proved, due to a ...
- 2,587
72
votes
7
answers
11k
views
Does gravity bend gravity?
Let's say that there is a large mass $M$ a light-year or so away from a black hole merger, which causes a very large gravitational wave to be produced. When the gravitational wave reaches $M$, does it ...
- 2,042
1
vote
0
answers
44
views
Electromagnetism, linearity and Feynman diagrams [duplicate]
Currently I am reading Sean Carrol, general relativity. But a thing got me stuck in, I can't understand what he is talking about.
We are discussing the introduction to Einstein field equation, so he ...
- 990
2
votes
0
answers
98
views
Is there a kink solution in general relativity?
In the special case of the $\phi^4$ scalar field theory in special relativity, a nice "kink" solution is very well known:
$$\tag{1}
\phi(z) = v \tanh \Bigl(\sqrt{\frac{\lambda}{2}} \: v \, z ...
- 7,677
2
votes
1
answer
315
views
In what physical situations is the weak-field limit invalid?
in the weak-field limit gravitation is described by a symmetric tensor field $h_{μν}(x)$ in flat spacetime. Linear theory suffices for nearly all experimental applications of general relativity ...
- 669
3
votes
0
answers
123
views
How to use Belinsky-Zakharov transformation
I know it might be trivial. When using BZ transformation [1] to generate soliton solutions of Einstein’s field equations, one need a seed solution $g_{0}$ which gives $A_{0}$ and $B_{0}$. Taking them ...
- 351
5
votes
1
answer
154
views
What are some experimental verification of the non-linearity of gravitation?
According to my (limited) knowledge, all experiments to date probe only situations which can be understood using the linearized version of general relativity. For example, measuring gravitational ...
- 2,646
21
votes
3
answers
4k
views
Is the universe non-linear?
First of all, I've read this other question Is the universe linear? If so, why? and I'm aiming at a different kind of answer.
Theories like General Relativity or QFT, which are believed to be quite ...
- 4,737
83
votes
13
answers
8k
views
Turbulent spacetime from Einstein equation?
It is well known that the fluid equations (Euler equation, Navier-Stokes, ...), being non-linear, may have highly turbulent solutions. Of course, these solutions are non-analytical. The laminar flow ...
- 7,677
5
votes
1
answer
657
views
Non-linearity and self-coupling of gravity
I have heard that non-linearity of Einstein's field equations has to do with the fact that gravity self-couples. What does non-linearity have to do with self-coupling?
- 877
0
votes
1
answer
517
views
Definition of "nonlinear" in the context of perturbation of gravity
What exactly is the definition of a nonlinear perturbation when applied to a background spacetime metric?
I have seen so called "linear perturbations" which look like
$$ds^2 = -(1+2\Phi)dt^2 ...
- 13
10
votes
3
answers
1k
views
Warp drive with gravitational waves in the nonlinear regime
gravitational waves are strictly transversal (in the linear regime at least), also their amplitudes are tiny even for cosmic scale events like supernovas or binary black holes (at least far away, ...
- 14.7k