# Tag Info

### 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

### 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

### 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

### 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
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

### 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