11
votes
What do we mean when we say gravitational waves are non-linear and do not superpose like EM waves?
The ordinary wave equation
$$\frac{\partial^2 u}{\partial t^2} = v_w^2 \frac{\partial^2 u}{\partial x^2}$$
where $u$ is the wave function and $v_w$ is the wave speed, is linear (in the sense of a ...
- 17.7k
8
votes
What do we mean when we say gravitational waves are non-linear and do not superpose like EM waves?
This simple definition is axiomatic:
The principle of superposition says:
When two or more waves cross at a point, the displacement at that point is equal to the sum of the displacements of the ...
- 223k
7
votes
What do we mean when we say gravitational waves are non-linear and do not superpose like EM waves?
The full Einstein equation is:
$$ G_{\alpha\beta} = 8\pi T_{\alpha\beta} $$
where $G_{\alpha\beta}$ is the Einstein tensor, which is a non-linear function of the metric. In general solving the ...
- 334k
4
votes
Does SXS catalog for NR simulations have non-spinning, non-eccentric blackholes?
All NR simulations (including the SXS simulations) have some eccentricity and some spin on each of the components. It is impossible to setup initial conditions where these vanish exactly.
However ...
- 8,262
3
votes
Accepted
Let $Q(t,\vec x)$ solve $\partial_t^2 Q = \nabla^2Q$. Why $\partial_t^2Q = 2 (\partial_r + r^{-1})\partial_{t-r}Q$?
You are not transforming the differentials correctly. $\partial/\partial t|_r=\partial/\partial u|_r$ and $\partial/\partial r|_t=\partial/\partial r|_u-\partial/\partial u|_r$.
- 947
2
votes
Do stars lose spin angular momentum, to planets, radiation, or gravitational waves, or in some other way get a longer period?
The main way that a star loses angular momentum is through a magnetised stellar wind. The highly ionised wind couples to the large scale magnetic field. This coupling is maintained out to some radius (...
- 113k
1
vote
Let $Q(t,\vec x)$ solve $\partial_t^2 Q = \nabla^2Q$. Why $\partial_t^2Q = 2 (\partial_r + r^{-1})\partial_{t-r}Q$?
The impeccable answer of @CWPP identifies the problem and leads to the straightforward correct answer; I'm only writing this as a footnote with an explicit expansion of his point to avoid the ...
- 48.9k
1
vote
Transverse component of distorsion tensor in GR
The paper you are referring to proves that any symmetric tensor field can be decomposed into transverse-traceless, longitudinal and trace parts, eq. 2 and 7.
$$ \psi_{ab} = \psi_{ab}^{\rm TT} + \psi_{...
- 1,058
1
vote
Question about gravitational waves
The ruler resists attempts to change its length, due to electrostatic forces between atoms in the ruler (eg see Young's modulus). This means the ruler will not change as length to the same extent as ...
- 35.4k
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