# Thread: Actual size of black holes

1. ## Actual size of black holes

`Hello Sciforums, I've been searching the net, and I can't seem to find a straight answer as to the size of black holes.

I know their masses differ, but does every black hole have the same volume, namely zero?

2. The size of a black hole is usually given in terms of its event horizon -- the surface of no escape. For a hypothetically non-rotating black hole, this volume is : $\frac{4 \pi}{3} R_s^3 = \frac{4 \pi}{3} \, \left( \frac{2 G M}{c^2} \right)^3 = \frac{32 \pi G^3 M^3}{3 c^6} \; \approx \; 1.07892009 \times 10^{\tiny 11} \, \textrm{m}^{\tiny 3} \, \left( \frac{M}{M_{\odot}} \right)^3 \; \approx \; 107.892009 \, \textrm{km}^{\tiny 3} \, \left( \frac{M}{M_{\odot}} \right)^3 \; \approx \; 25.9 \, \textrm{mile}^{\tiny 3} \, \left( \frac{M}{M_{\odot}} \right)^3$

While we think of black holes as being super-dense, this definition of volume makes bigger black holes less dense than smaller black holes.

The other definition of volume is for the inaccessible singularity of General Relativity, which is conventionally understood to be of zero volume.

http://pdg.lbl.gov/2011/reviews/rpp2...-constants.pdf

3. JM123

As to what we can see in this Universe, RPenner's explanation is correct(as usual). But as to the size of the actual "singularity" the honest answer is "We have no real idea", mainly because we can't see it at all and can have no real idea of the physics involved inside the event horizon. There may be a stopping point for density, there may not be. Personnally, I don't think infinities exist except as a concept that really indicates nothing but the limits of what we can know. Time had a beginning and has not yet ended, thus finite, same goes for space. I have a speculation that what goes into BHs comes out at the Big Bang, being connected to that point in time and that point only(thus avoiding "Grandfather Paradoxes")by the other half of the half dimension of time we experience(we can travel in both directions through all three of the space dimensions, but only one way through time), that the theoretical wormholes(supposedly leading to "White Holes")lead to the only White Hole we know exists, the Big Bang. But I will admit up front I have no way to evidence this, even though it would tie up some stubborn loose ends in physics.

Grumpy

4. .... mainly because we can't see it at all and can have no real idea of the physics involved inside the event horizon.
we know the physics inside the event horizon down until quantum effects become dominant.

5. Originally Posted by Boris2
we know the physics inside the event horizon down until quantum effects become dominant.
This is just not true. It is very often, even among those who would be considered experts, a tendepancy to forget the difference between what we know and what we believe.

Within this context, a great deal of what happens at or just outside the event horizon of a black hole remains theoretical. Which is the same as saying, it is "what we believe". What happens inside the event horizon is a step further from anything we can say we know for certain.

Black holes emerge from general relativity, not quantum mechanics.., and general relaitiviy tells us nothing of what happens at the subatomic scales of quantum mechanics. Even at the event horizon of a black hole where general relativity should remain a valid predictor of the spacetime conditions present, quantum mechanics better describes some of what we believe is going on. No one has yet successfully unified GR and QM. Until such time as this can be done, there are a great many things about physics that must remain filed in the category of, "to the best of our knowledge".

So, to say, "we know the physics inside the event horizon down until quantum effects become dominant." is very much like saying we know what is going on inside a black hole down to a the scale of a theory that does not explain what is going on inside a black hole. We have no successful quantum theory of gravity and we do not even, know the form, structure and relationship of matter and energy, under the conditions inside the event horizon of a black hole. Even what is happen AT the event horizon remains mostly theoretical.

There are a great many things in physics that I am personally not an expert on. Some of those I accept on faith. Faith in the knowledge and understanding of others, who I believe are experts... Still, and I have said this before, it is always important to remember the difference between what we know for certain and what we believe or think we know, because it seems a logical extension of what we do know or a reasonable application of our best theoretical understanding.

6. OnlyMe, you're quite incorrect.

Quantum mechanics becomes dominant (specifically quantum gravity) when you're a few Planck lengths from the centre of the black hole but unless you're dealing with an extremely small black hole the event horizon is not that close to the centre. At the event horizon quantum phenomena like Hawking radiation exist but there's a very very small effect. For example, the brightness of the old filament bulbs is due to them being heated to thousands of degrees but the energies involved are pretty low. A black hole of stellar mass is less than 1K in temperature so it's not going to be pumping out much in the way of energy so quantum produced phenomena will be quite weak.

As for inside the black hole there's ways in GR (Eddington coordinates or Kruskal coordinates) of continuously tracking the behaviour of an infalling object from above the event horizon, onto the event horizon and then inside it. If you accept what GR says about things outside the event horizon then you have no reason to reject what it says about inside the event horizon but far from the centre, as quantum corrections are completely insubstantial.

What happens at the event horizon is typically very boring as it happens, it's all to do with local frames. Things like tidal forces ripping an object apart do not require considering the event horizon. A sufficiently massive black hole will have weaker forces at it's event horizon than you and I are currently experiencing sitting in our chairs in front of our computers on Earth right now.

Yes, all of this is hypothetical since we don't have a black hole to hand to test it but if you accept what GR says above the event horizon then you would be self contradicting if you rejected what it says about the event horizon and just inside the event horizon. Yes, quantum effects have parts to play but except for extremely small black holes where the event horizon is within a few Planck lengths of the singularity the quantum effects near and just under the event horizon are little corrections, like Hawking radiation.

7. Originally Posted by AlphaNumeric
OnlyMe, you're quite incorrect.
I am not quite sure what aspect of my previous post you are referring to. Nothing in your post is actually contrary to anything in mine. Yes isolated statements out of context may be questionable, but the same applies to your response.

In context my comment(s) were in response to this statement, "we know the physics inside the event horizon down until quantum effects become dominant." The statement represents an absolute, which lacks any experimental or observational confirmation.

The idea of what we know, what we think, what we believe and, as I often phrase it, "what we think we know", is the key point being addressed. Since we have no direct evidence of black holes, meaning we can only project their existence by the affect that they have on other objects, everything we know about black holes, their event horizons, just inside and outside of their event horizons, is based on hypothesis and theory. Even then, there is not complete agreement, we have multiple models, hypothesis and theories, all addressing, what we think occurs...

You ended your above post with a statement, of essentially, at least as I read it, the same intent, as the point of my post,
Originally Posted by AlphaNumeric
Yes, all of this is hypothetical since we don't have a black hole to hand to test...
The best post in this thread so far was the second post by rpenner,

Originally Posted by rpenner
The size of a black hole is usually given in terms of its event horizon -- the surface of no escape. For a hypothetically non-rotating black hole, this volume is : $\frac{4 \pi}{3} R_s^3 = \frac{4 \pi}{3} \, \left( \frac{2 G M}{c^2} \right)^3 = \frac{32 \pi G^3 M^3}{3 c^6} \; \approx \; 1.07892009 \times 10^{\tiny 11} \, \textrm{m}^{\tiny 3} \, \left( \frac{M}{M_{\odot}} \right)^3 \; \approx \; 107.892009 \, \textrm{km}^{\tiny 3} \, \left( \frac{M}{M_{\odot}} \right)^3 \; \approx \; 25.9 \, \textrm{mile}^{\tiny 3} \, \left( \frac{M}{M_{\odot}} \right)^3$

While we think of black holes as being super-dense, this definition of volume makes bigger black holes less dense than smaller black holes.

The other definition of volume is for the inaccessible singularity of General Relativity, which is conventionally understood to be of zero volume.

http://pdg.lbl.gov/2011/reviews/rpp2...-constants.pdf
Note: He mentions two theoretical models for black holes. First a "hypothetically non-rotating black hole", which may exist only within the hypothetical, as it would be a reasonable bet to assume that all black holes do rotate. And then second, "the inaccessible singularity of General Relativity". Neither of these or any other black hole model has been confirmed, as far as the internal structure, of the involved mass, or even the mechanics of the event horizon. These things remain beyond the current limitations of our ability to observe.., directly. They remain, in the realm of, "what we think we know".

You did raise two points that are of interest, to me personally.

Originally Posted by AlphaNumeric
A sufficiently massive black hole will have weaker forces at it's event horizon than you and I are currently experiencing sitting in our chairs in front of our computers on Earth right now.
Do you believe this to be generally accepted, as more than a mathematical possibility? Without, confirmed knowledge of the internal mechanics and physics of a black hole, the assertion is presented with too much certainty. And it is not consistent with any experience we do have with gravitational forces and escape velocities. There are too many assumptions involved in that solution, for it to be presented, as an absolute.

Originally Posted by AlphaNumeric
... If you accept what GR says about things outside the event horizon then you have no reason to reject what it says about inside the event horizon but far from the centre, as quantum corrections are completely insubstantial.
This would seem to be a logical assumption, but there is a trap in the logic. If we agree, that by accepting what GR says about things outside the event horizon, GR automatically and unquestionably applies to what happens within the event horizon, the same logical application of GR cannot be ignored when it comes to subatomic scales, where we know that it does not result in conclusions and predictions, that are consistent with experience. The field equations of Einstein and/or Newton, if applied to the mass densities and distances involved with protons and neutrons, return irrational results and infinite gravitational forces. Atoms could not exist, but they do, so we just don't go there... We cannot just assume... Don't get me wrong here I am not trying to say that, "what if" scenarios are not valid and useful. What I am saying is that it is important to remember the difference between, "what we know" and have confirmed through experience, and "what we THINK we know", because it seems to follow logically from theory.

8. It seems unreasonable to not accept the predictions of GR for regions beyond the Event Horizon, but far from the so called singularity.

Of course, hardly any credible physicist accepts the concept of an infinitely dense point mass at the center. I suspect that even GR provides no basis for denying a limiting density. Id est: It merely seems convenient to extraoplate GR equations to a singularity & then state that infinite density strongly impies that GR is no longer valid in some region close to the center of a typical black Hole.

BTW: When an oscillating BigBang/CatastrophicCrunch theory was considered a possible cosmology, it was postulated that the Universe would appear to be a Black Hole to an external observer.

The above speculation implies that GR allows for a long period of ordinary activity within a large Event Horizon.

9. Something needs to be kept in mind about Event Horizons in the time frame of the outside Universe. Yes, an infalling observer would experience no dramatic change as he crossed the EH, but to the rest of the Universe he never crosses that Horizon at all and this is not just an appearance, it is a physical reality. Everything that has ever fallen into any Black Hole is still falling today, from the perspective of any outside observer, time stops dead at the Event Horizon. This represents the extreme of Relativity, just as the speed of light represents another extreme with similar effects. All of the effects BHs can display occur outside of that Event Horizon with the exceptions of the curvature of space by mass, possibly frame dragging due to rotation and possible charge. Singularities may not form simply because there hasn't been enough time to do so(and there may never be enough time).

Grumpy

10. Originally Posted by Grumpy
Something needs to be kept in mind about Event Horizons in the time frame of the outside Universe. Yes, an infalling observer would experience no dramatic change as he crossed the EH, but to the rest of the Universe he never crosses that Horizon at all and this is not just an appearance, it is a physical reality. Everything that has ever fallen into any Black Hole is still falling today, from the perspective of any outside observer, time stops dead at the Event Horizon. This represents the extreme of Relativity, just as the speed of light represents another extreme with similar effects. All of the effects BHs can display occur outside of that Event Horizon with the exceptions of the curvature of space by mass, possibly frame dragging due to rotation and possible charge. Singularities may not form simply because there hasn't been enough time to do so(and there may never be enough time).

Grumpy
No Grumpy, it's an illusion caused by the infinite red-shifting of the last photon before the infalling observer crosses the event horizon. The remote observer would see time slowed in the infalling observer's space ship, but that time is slowed within the observers's frame of reference. But the frame itself (i.e. the ship) is moving relative to the observer, and it doesn't stop moving.

To support this, I refer you to Kip Thorne's Black Holes and Time Warps. I'd give you the actual pages, but my copy was lent to my son, which means I have to buy another one.

11. Grumpy: I have seen many variations on the following, which (if not dead wrong) is very misleading.
Something needs to be kept in mind about Event Horizons in the time frame of the outside Universe. Yes, an infalling observer would experience no dramatic change as he crossed the EH, but to the rest of the Universe he never crosses that Horizon at all and this is not just an appearance, it is a physical reality. Everything that has ever fallen into any Black Hole is still falling today, from the perspective of any outside observer, time stops dead at the Event Horizon.
The Red Bolded part of the above is dead wrong. It might (likely is) valid to claim that an outside observer never "sees" mass falling past the Event Horizon.

In several threads, I have posted explanations of how Event Horizons grow in finite time & how objects can cross an Event Horizon in finite time. I never posted supporting calculated numbers & seem to have been ignored.

If you do not trust the following calculations, search for the pertinent equations & do the arithmetic. I did the calculations with MathCad 7 (A poor man’s Mathematica, which is almost as good as later versions of MathCad.).

Event Horizons grow in finite time. This is a fact derivable from simple logical analysis & can be backed up with actual calculations.
Consider a Black Hole whose mass is one million Solar Masses: Event Horizon radius is approximately 2.968 billion meters.

Consider a Black Hole whose mass is 1.1 million Solar Masses: Event Horizon radius is approximately 3.265 billion meters.

Difference in radii: 0.297 billion meters

If (actually when) 100,000 solar masses get within 3.265 billion meters of the center of the Black Hole, the Event Horizon will have increased by 0.297 billion meters.
I am sure that many galaxies have central Black Holes containing more than one million solar masses. Actually, I think that there are galaxies whose central Black Hole contains a billion or more solar masses.

A Black Hole at the center of a galaxy could be expected to attract an additional 100,000 solar masses in finite time. As it did so, the Event Horizon would grow by about 0.297 billion meters.

An external observer would not ”see” any mass crossing the original Event Horizon. He could however ”see” The Event Horizon growing in finite time. Some of the objects he ”saw” falling toward the original Event Horizon would be inside the current Event Horizon & very likely pulled past the original Event Horizon.

BTW: The density of the volume included within the Event Horizon, decreases as the mass of the Black Hole increases. The radius is a linear function of mass, while the volume increases as the cube of the mass. Id est: Volume increase is proportional to the cube of mass.

12. Originally Posted by OnlyMe
Originally Posted by AlphaNumeric
What happens at the event horizon is typically very boring as it happens, it's all to do with local frames. Things like tidal forces ripping an object apart do not require considering the event horizon. A sufficiently massive black hole will have weaker forces at it's event horizon than you and I are currently experiencing sitting in our chairs in front of our computers on Earth right now.

Do you believe this to be generally accepted, as more than a mathematical possibility? Without, confirmed knowledge of the internal mechanics and physics of a black hole, the assertion is presented with too much certainty. And it is not consistent with any experience we do have with gravitational forces and escape velocities. There are too many assumptions involved in that solution, for it to be presented, as an absolute.
Yes, it is accepted. The event horizon of a BH is nothing special. The physics, while near the limits of physical laws, is still quite mundane. It is a calculated point at a distance from the centre where escape velocity exceeds c. That's all. A freely falling observer would experience nothing untoward as they crossed it. They wouldn't even know it.

A loose analogy: Say I am in a rocket, falling toward the Earth. My rocket has only enough fuel to reach 8km/s velocity. Escape velocity at Earth's surface is 11km/s That means, as I fall toward Earth, there will be a point below which I can no longer escape. There is absolutely nothing else special about that altitude. In fact, the only way I will have any idea when I cross it is by calculating it.

So, the event horizon of a BH is certainly significant to external observers, and it has something to say about the future prospects of a local observer, the local observer experiences no significant difference between passing an 'EH+20 mile' marker, and 'EH+10 mile' and and 'EH-10 mile' marker.

13. Dinosaur

The point is the two different frames experience time at very different rates relative to each other. The frame travelling into the BH will experience less time than the frame not in the gravity well. It is not just the appearance of time stopping at the EH, it actually slows to a stop as seen from the frame of the Universe as a whole. Yes, mass is gained by the expansion of the EH, consuming mass that would never otherwise reach the EH on it's own.

And it is really unimportant to this point what the density inside the EH is, the EH is not a structure, it is simply the radius from the center of mass where the escape velocity is the speed of light. It is an end point to our Universe. If the BH is big enough you would not notice when you crossed it(except for the freaky light show effects), but the outside observer would see the same effects no matter what the size, the size only makes a difference in what the one going into the hole would experience.

Grumpy

14. Originally Posted by DaveC426913
Yes, it is accepted. The event horizon of a BH is nothing special. The physics, while near the limits of physical laws, is still quite mundane. It is a calculated point at a distance from the centre where escape velocity exceeds c. That's all. A freely falling observer would experience nothing untoward as they crossed it. They wouldn't even know it.

A loose analogy: Say I am in a rocket, falling toward the Earth. My rocket has only enough fuel to reach 8km/s velocity. Escape velocity at Earth's surface is 11km/s That means, as I fall toward Earth, there will be a point below which I can no longer escape. There is absolutely nothing else special about that altitude. In fact, the only way I will have any idea when I cross it is by calculating it.

So, the event horizon of a BH is certainly significant to external observers, and it has something to say about the future prospects of a local observer, the local observer experiences no significant difference between passing an 'EH+20 mile' marker, and 'EH+10 mile' and and 'EH-10 mile' marker.
My question was not to the issue you seem to be addressing or that portion Alpha mentioned earlier. I was questioning only the following portion,

Originally Posted by AlphaNumeric
... A sufficiently massive black hole will have weaker forces at it's event horizon than you and I are currently experiencing sitting in our chairs in front of our computers on Earth right now.
True if you were falling through an event horizon there should be no meaningful difference other than those Alpha mentioned earlier.., as in apart from tidal effects. However, if the escape velocity equals or exceeds c, then there are forces involved greater than those we experience locally.

It would seem that only where you are talking about free fall conditions, would the involved forces, "experienced", be the same or similar. Set your self into a spaceship and try to escape, even if you fail the gravitational interaction would seem logically to be about as absolute as you can get.

And all of this assumes that even in free fall conditions any issues the velocities that would be involved would have no independently measureable impact.

#### Posting Permissions

• You may not post new threads
• You may not post replies
• You may not post attachments
• You may not edit your posts
•