# Thread: Do black holes have volume

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## Do black holes have volume

Are they a singularity or do they have volume? If they are a singularity, why do so many articles say that if the Earth was compressed to the size of a marble, or something comparable, it would create a black hole? That implies volume, not event horizon.

2. Once you get enough mass inside the radius of that mass' event horizon, a black hole will form. Does the mass collapse to a singularity? That isn't known. It might be a singularity (Pure General Relativity), or there may be some small size that is a minimum radius, or it might be something else (e.g. Firewall at the EH). One of the hopes of the ALIGO & VIRGO (and eventually other) Gravitational Wave observatories is to make observations that will give more clues about this, so that eventually we might know the answer to your question.

3. The "size of a marble" idea is based on a measure called the "reduced circumference" of a Schwarzschild black hole event horizon. If an observer could hover at the event horizon (they can't) and lay out metre rules around the circumference of a non-rotating black hole at that distance, they'd get a value for the circumference. Divide by 2 pi, and you get a corresponding radius, which you can't measure directly. That's the "reduced circumference", and it turns out to be equal to the radius of the event horizon as measured in a particular set of coordinates, called Schwarzschild coordinates, which can be referred to a distant, stationary observer. That's why you'll commonly see the reduced circumference referred to as the Schwarzshild radius of the black hole. Plugging that into the familiar equation for the volume of a sphere, 4/3 pi r3, gives you a measure of volume below the event horizon, in Schwarzschild coordinates.
But observers in different states of motion at different distances from the black hole measure different distances and times - the Schwarzschild coordinates are merely "book-keeping" coordinates, and no observer in the vicinity of the event horizon will experience distances in that coordinate system. So the radius and volume below the event horizon are slippery concepts with no unique answer, and there are useful coordinate systems in which there is zero volume below the event horizon.

There's a theorem that shows, according to our current physics, that if you compress any mass to within its Schwarzschild radius, it will inevitably collapse under its own gravity to form a singularity. Which is where we get the commonly expressed idea that if you compress a mass to [some size corresponding to its Schwarzschild radius], a black hole will form. But as antoniseb says, we don't actually have the physics to know what happens at extreme densities, and something may prevent a final mathematical singularity forming within the event horizon.

Grant Hutchison

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Thanks for the responses.

So, saying an Earth compressed to a marble like size, or the Sun down to around 4 miles in diameter, is expressing the event horizon, not the actual spherical mass?

This further confused me cause black holes are expressed in terms of densities, which volume is needed.
Last edited by dnj123; 2018-Nov-17 at 01:52 PM.

5. Originally Posted by dnj123
Thanks for the responses.

So, saying an Earth compressed to a marble like size, or the Sun down to around 4 miles in diameter, is expressing the event horizon, not the actual spherical mass?
That's right. Once you get it down to the size of the event horizon, physics predicts it has to keep on getting smaller towards the singularity. So "compress to the size of the marble and you get a black hole" is really saying that the event horizon forms at that size, and the mass will continue to collapse inside the event horizon.

Originally Posted by dnj123
This further confused me cause black holes are expressed in terms of densities, which volume is needed.
It would be good if people didn't talk about densities, but it's a common enough idea in popular science descriptions. Basically they're dividing the mass by a volume naively calculated from the Schwarzschild radius. Given that all the mass is predicted to be down in the singularity, and the volume beneath the event horizon is coordinate-dependent, the "density" of a black hole is a pretty meaningless concept at best, and actively misleading at worst.

Grant Hutchison

6. Welcome to modern physics, in all of its mind-blowing glory, and beware of bad popular media writing on the topic.

7. and beware of bad popular media writing on the topic.
And even good popular writing!

8. I've posted this link before in another thread, but it's quite a useful illustration of the problematic nature of black hole "volume": DiNunnio & Matzner, "The Volume Inside A Black Hole" (2008).
The surface area of the event horizon is much better defined, and much more physically important.

Grant Hutchison

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Thank you all, you've been very helpful.

10. Originally Posted by dnj123
...if the Earth was compressed to the size of a marble, or something comparable, it would create a black hole? That implies volume, not event horizon.
A simpler way to look at it might be to say that a black hole - the object - is generally understood to have its EH as its "size". It's just that not all of a black hole is mass.

A galaxy has a volume too, but not all of its volume is mass.

Unlike solid bodies, volume in these cases is an arbitrary man-made bounding shape.
Last edited by DaveC426913; 2018-Nov-17 at 06:59 PM.

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Einstein doubted the singularity. He said the physical mass would stop the collapse at some point. But it's unreal either way.

I'm sorry if this is old news, this is just mind blowing to me:

12. Wouldn't the recent detection of gravity waves from black hole mergers tell us that the mass in black holes are not infinitessimally small volume-wise? They have a peak frequency and peak amplitude before the merging of the masses finalises and the energy emitted by gravity waves settles down.
Last edited by Xelebes; 2018-Nov-19 at 03:08 AM.

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Originally Posted by dnj123
Einstein doubted the singularity. He said the physical mass would stop the collapse at some point. But it's unreal either way.
When black holes were first proposed many astrophysicists doubted their existence because of the singularity. Their solution was some process to stop the collapse. However by the 1960's (after Einstein's death), we had discovered neutron stars and there was no mechanism to stop a neutron star from collapsing to a black hole by gaining mass, e.g. by sucking it from a companion star. Today the empirical evidence is strong that black holes exist.
Pointed Debate by astrophysicist Brian Koberlein covers this subject.

Note that the classical GR singularity may become "fuzzy" on quantum scales in a quantum gravity theory so we may find that black holes do not contain singularities.

The Stuff Falling into This Black Hole Is Moving at Almost 56,000 Miles a Second! is interesting new science.

14. Originally Posted by Xelebes
Wouldn't the recent detection of gravity waves from black hole mergers tell us that the mass in black holes are not infinitessimally small volume-wise? They have a peak frequency and peak amplitude before the merging of the masses finalises and the energy emitted by gravity waves settles down.
No information from inside the event horizon will escape. The information we receive will only be from outside the EH.

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