41
votes
Accepted
Do black holes have a moment of inertia?
The angular velocity of a Kerr black hole with mass $M$ and angular momentum $J$ is
$$ \Omega = \frac{J/M}{2M^2 + 2M \sqrt{M^2 - J^2/M^2}} $$
The moment of inertia of an object can be thought of as ...
- 6,475
35
votes
Accepted
Wouldn't Miller's planet be fried by blueshifted radiation?
Miller's world would be fried by a strong flux of extreme ultraviolet (EUV) radiation. The cosmic microwave background (CMB) would be blueshifted by gravitational time dilation and then would be very ...
- 135k
32
votes
Accepted
What do black holes spin relative to?
But if you start running around it, it will move faster or slower relative to you.
In this case, the disc has a ground speed, 60 rpm, because it has something to spin in relation to, in this case, the ...
- 105k
30
votes
Accepted
Massless Kerr black hole
It's simply flat space in Boyer-Lindquist coordinates. By writing
$\begin{cases}
x=\sqrt{r^2+a^2}\sin\theta\cos\phi\\
y=\sqrt{r^2+a^2}\sin\theta\sin\phi\\
z=r\cos\theta
\end{cases}$
you'll get good ol'...
- 5,951
29
votes
Accepted
Can a Kerr black hole become super-extremal?
TLDR; No, it cannot.
The answer to this question has a somewhat storied history.
Back in 1974 Wald considered a Gedanken experiment of what would happen if you would try to drop an object into a Kerr ...
- 12.6k
27
votes
Why does Roy Kerr claim that the Kerr black hole does not contain a singularity?
As far as I can tell, Kerr's point is that the singularity theorem doesn't specify whether or not a collapsing object will collapse to a "real" singularity. As a reminder, singularity ...
- 16.6k
24
votes
Why are complex coordinates outlawed in physics?
are complex coordinates completely outlawed in physics?
Complex coordinates are “outlawed” specifically in general relativity, which is the relevant physics for your question.
The mathematical ...
- 105k
16
votes
Massless Kerr black hole
This is presumably a flat spacetime described in funny coordinates. You can check this by calculating the Riemann tensor to see if it's zero. If I was going to do this, I would code it in the open-...
- 161
13
votes
Why does Roy Kerr claim that the Kerr black hole does not contain a singularity?
The central point of Kerr's paper is showing examples of inextendible null geodesics with finite affine length that do not end in a singularity. To construct such an example he looks at null geodesics ...
- 12.6k
12
votes
Accepted
How does the Penrose diagram for a spinning black hole differ in realistic scenarios (formed by stellar collapse)?
Your question basically boils down to a recognition of the following fact:
The Schwarzschild metric, with spacelike $r=0$, admits an "eternal" BH to form by stellar collapse, like the one you've ...
- 1,456
12
votes
Why does Roy Kerr claim that the Kerr black hole does not contain a singularity?
There are some answers here that do a good job of exhibiting the curves that Kerr has pointed out, but I don't think any have outlined his core argument in a faithful manner, and most have missed key ...
- 1,300
11
votes
Does the twist of spacetime by a black hole increase over time?
The spacetime around a rotating black hole (Kerr metric) is stationary, this means that you can choose a coordinate system where the metric doesn't depend on the time coordinate. In layman's terms ...
- 2,919
11
votes
What happens to the ring singularities when two Kerr black holes merge?
The ring singularity in Kerr is something that exists inside the inner horizon. Therefore the ring singularity exists only in the future of anyhting that happens outside of the black holes, including ...
- 12.6k
10
votes
Killing tensor in the Kerr metric
The Killing tensor is defined as a symmetric tensor $K_{\alpha \beta}$ whose total symmetrization of the covariant gradient vanishes
$$K_{(\alpha \beta;\gamma)} = K_{\alpha \beta;\gamma} + K_{ \beta\...
- 20.5k
9
votes
Accepted
Event horizon of a rotating black hole
The event horizon' radius of black holes is an infinite-redshift surface (a one-way surface where particles can never
escape to infinity). It can be computed analytically (or at least numerically) by ...
- 4,600
9
votes
Accepted
Does the twist of spacetime by a black hole increase over time?
Yes, you are taking the metaphor too literally. When we visualize spacetime like a flexible rubber sheet there is an accidental and erroneous impression that a twist will lead to spacetime getting ...
- 33.1k
9
votes
Accepted
Are rotating black holes producing a frame dragging effect inside the event horizon?
Krešimir Bradvica asked: "Are rotating black holes producing a frame dragging effect inside the event horizon? Is that effect moving space inside the event horizon at speeds far greater than the ...
- 12.5k
9
votes
Why are complex coordinates outlawed in physics?
Many physical theories use complex numbers. Quantum mechanics is the obvious example, but even everyday theories like circuit theory use complex numbers, and then we have the more esoteric theories ...
- 359k
8
votes
Do black holes have a moment of inertia?
Moments of inertia are defined about a given axis of rotation.
Moment of inertia is the name given to rotational inertia, the rotational analog of mass for linear motion. It appears in the ...
- 235k
8
votes
Accepted
Exceeding the Kerr black hole spin limit
This is an interesting question that could really be formulated as follows:
When collapsing an object that has the ratio $a^* = cJ/(GM^2)$ larger than one, can an over-extremal black hole form?
...
- 20.5k
7
votes
Area of the event horizon of a rotating black hole
If you write the element surface as:
$d\sigma$ = $dl_{\theta}$ $dl_{\phi}$
you should have:
$dl_{\theta}$ = $\sqrt{g_{\theta\theta}}$ $d\theta$
$dl_{\phi}$ = $\sqrt{g_{\phi\phi}}$ $d\phi$
Hence the ...
- 3,806
7
votes
Accepted
What is exactly rotating in a rotating black hole?
So let us first ask ourselves: What makes us believe that anything is rotating in the Kerr space-time?
The answer is that we go very far away from the black hole and look at the asymptotics of the ...
- 20.5k
7
votes
What do black holes spin relative to?
This is just Newton's bucket in modern garb. The best explanation of this effect that I have seen is in Carlo Rovelli's book Quantum Gravity, which explains it as rotation with respect to the ...
- 381
7
votes
Accepted
Black holes in general relativity: angular velocity of the horizon
As a warm-up, consider the non-rotating case $\Omega_H=0$. From the perspective of a distant observer, any pointlike test object that falls into a non-rotating black hole will appear to freeze at the ...
- 54.7k
7
votes
Wouldn't Miller's planet be fried by blueshifted radiation?
For a 2.7 K blackbody (like the CMB) the calculator at
http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/radfrac.html
gives me 3 $\mu$W/m$^2$. This is how much Earth is heated by the CMB — not a lot!
...
- 943
6
votes
Accepted
How can a black hole rotate if time dilation stops time at the event horizon?
The statement "time is dilated to infinity at the horizon" is a (very imprecise) way of saying that the event horizon is a null/lightlike surface. However, as is clear from light-rays, being ...
- 12.6k
6
votes
Accepted
What's the inner ergosphere in a Kerr black hole?
If you are learning about the Kerr geometry I strongly recommend Matt Visser's paper The Kerr spacetime: A brief introduction as he manages to pack in all the essential information and still keep it ...
- 359k
6
votes
Why is Kerr Spacetime unstable?
That is a very good question. I will give you a rough argument of why we believe this to be true based on Bob and Alice. You can find a more detailed discussion at e.g. https://www.jstor.org/stable/...
- 570
6
votes
Why does Roy Kerr claim that the Kerr black hole does not contain a singularity?
Kerr writes:
The original Kerr-Schild coordinates were deliberately chosen to be a generalisation of Eddington’s, avoiding any coordinate singularities on either horizon. It will be shown in Section ...
- 28.1k
5
votes
Closed timelike curves in the Kerr metric
Let me write down the metric in the equatorial plane ($\vartheta = \pi/2$) of the Kerr space-time in Boyer-Lindquist coordinates:
$$
d s^2 = -\left(1 - \frac{2M r}{r^2 + a^2}\right) d t^2 + \frac{r^2+...
- 20.5k
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