Exploring Black Hole Anatomy: The Singularity, Event Horizon, and Photon Sphere

In summary, there are several theories about the nature of black holes, particularly regarding the singularity at its center. The standard model describes the geometry with a singularity surrounded by an event horizon and a photon sphere. It is possible to calculate the distance and ratios between these three components using mathematical equations, but it is not considered an easy task. The general consensus is that the singularity has no actual size or diameter and is of infinite density. However, some speculative physics models, such as String Theory, suggest the singularity may have a finite density and therefore a calculable diameter. General Relativity, while able to describe the area around a black hole, breaks down at the singularity and cannot accurately explain its behavior. It is believed that
  • #1
bill alsept
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I know there are several theories as to what may be inside black holes and that the standard model usually describes the geometry with a singularity surrounded by an event horizon and then a photon sphere.
Three questions:

Is there an easy way to calculate the distance and or ratios between the three?

Does the singularity have an actual size (diameter) like the other two?

Is the singularity always a point or are there any theories that model the singularity with an actual diameter that continues to grow as it accumulates matter?
 
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  • #2
Singularities aren't well described by modern physics. General Relativity can describe the area around a singularity (a black hole), but the mathematics of GR give nonsensical answers at the singularity itself.

In terms of mathematics of the distance and ratios; yes, but I don't know them and 'an easy way to calculate' is probably not realistic: Einstein was a genius for a reason. The event horizon is simply the point around a mass where the escape velocity = c (the speed of light). While I know that some speculative physics models describe singularities differently (String Theory in particular), I believe the quasi-accepted current view on singularities is that they are points of no diameter and of infinite density.
 
  • #3
The Swarzschild radius gives you the basic relationship.
 
  • #4
How does the swarzchild radius describe the relation of all three? Is there some proportionality between their radiuses?
This question becomes more interesting if we imagine a singularity with a finite density and therefore an actual diameter. How then would the three diameters compare?
 
  • #5
I don't think we can realistically trust General Relativity to give the correct answer to the behavior of a black hole inside the event horizon, unfortunately.
 
  • #6
What if we just assume it is like any other mass? The fact that its g has an escape velocity of c doesn’t necessarily mean the body of the black hole has to be a point. If the singularity had a finite density and therefore a diameter would there be a way to calculate that diameter based on the mass?
 
  • #7
bill alsept said:
What if we just assume it is like any other mass? The fact that its g has an escape velocity of c doesn’t necessarily mean the body of the black hole has to be a point. If the singularity had a finite density and therefore a diameter would there be a way to calculate that diameter based on the mass?
Once you have enough mass in small enough an area to form a black hole, the pressure required to keep the matter collapsing actually increases the gravity, so that it becomes fundamentally impossible for any amount of pressure to prevent the collapse.
 
  • #8
Why is pressure required to keep the matter collapsing? Did you mean keep the matter FROM collapsing? If something becomes 100% dense (as I believe the singularity to be) and cannot get any denser then how can it collapse any farther? And why would it need pressure to keep it from collapsing?
 
  • #9
Chronos said:
The Swarzschild radius gives you the basic relationship.
To expand on this response (to make it even vaguely useful), the event horizon, photon sphere, and other interesting surfaces can all be easily calculated in GR for any type of black hole---with the different surfaces generally expressed in terms of the Schwarzschild radius (and other fundamental parameters, i.e. spin and charge).

Chalnoth said:
I don't think we can realistically trust General Relativity to give the correct answer to the behavior of a black hole inside the event horizon, unfortunately.
Just to clarify, GR Is well behaved within the event horizon, its only near the singularity that it breaks down. In the case of a rotating or charged black hole, it can be a little worse.

bill alsept said:
The fact that its g has an escape velocity of c doesn’t necessarily mean the body of the black hole has to be a point.
According to GR, the central mass does need to be a point. Not only is the escape velocity equal to 'c'; but also, space-time is so distorted inside the event horizon that the only direction a particle can move is inward (i.e. its 'impossible' to even stay still--like on a hard surface).

bill alsept said:
Why is pressure required to keep the matter collapsing? Did you mean keep the matter FROM collapsing? If something becomes 100% dense (as I believe the singularity to be) and cannot get any denser then how can it collapse any farther? And why would it need pressure to keep it from collapsing?
He did mean "keep the matter 'from' collapsing". Pressure is always required to keep material from collapsing. The reason the Earth doesn't collapse, or the air in the room, or the table your typing on---are because of pressure. Once inside the event horizon there is no pressure strong enough to resist collapse (according to general relativity). There is no such thing as '100%' dense---something can become arbitrarily dense because it can become arbitrarily small.

People think that a new quantum theory of gravity might be able to explain what actually happens at the singularity. Most string theorists, for example, think that at some point the matter will reach a maximum density (and minimum size), at about the Planck scale---[itex]\sim 10^{-35} m[/itex]; but no one really knows.

An additional thing to note is that charged and rotating black-holes have singularities that aren't points. A rotating black hole (called a "Kerr black hole") actually has a torus-shaped singularity (again, according to GR) with a finite, calculable size.
 
  • #10
I realize pressure is required to keep stars and anything else that may have space inside from collapsing. My point is that a singularity MAY be as dense as anything can be. It can't collapse anymore and therefore would need no pressure to support it. If this were possible then the singularity would have an actual size and would be growing proportionately just like the event horizon and photon sphere. My original question was how could you calculate the diameter of the singularity? Hypothetically speaking.
 
  • #11
bill alsept said:
It can't collapse anymore and therefore would need no pressure to support it.

Incorrect. Not only can it collapse further, it has to. The whole weirdness of a singularity stems from the fact that its a point of infinite density.
 
  • #12
How can it collapse further and why does it have to? Can't a black hole be so dense that there is no space left inside? An area filled 100% complete with the smallest partials the universe has to offer. There would be no more area to collapse to.

I realize my original question most likely cannot be answered because we don’t know how small those first particles are or how many have accumulated in the black hole. Could there be some indirect way to calculate backwards from the observed mass and event horizon and come up with either a diameter for the singularity or something.

We may need to think out of the box and ignore GR on this one.
 
  • #13
Well ignoring GR whilst trying to calculate black hole information is like asking someone what color a house is without looking at it, but I can address your other point.

Fundamental Particles don't really have a size, when you start getting down to the level where the size of a Fundamental particle becomes non-trivial, the uncertainty principle takes over. Basically a fundamental particle is a point-particle which means it is zero-dimensional (no size), but the uncertainty principle enters in and instead of a single point where the particle definitely is, you have a range of different points where the particle could be located (if that didn't make sense search the forums, someone has explained it better than me). A simple way of looking at it is that as density increases the width of those possible locations of the particle gets smaller. Within a black hole the gravitational force is so great that no force in the universe (that we know of) is strong enough to counter the inward push of gravity. So normally when particles are pushed together, the probability clouds of the particles (meaning the patch where the particle could be) get smaller until some other force (electromagnetic, strong, weak) pushes outwards and balances the force of gravity. However in a black hole, there is no force strong enough to counter the push of gravity so the probability waves of the particles get infinitely small.
 
  • #14
I hope I am not hijacking a thread here, but it seemed appropriate to ask here rather than creating a new thread...

how do black holes gain mass, or merge with another, if nothing can be observed to enter the BH in finite time? Do they get bigger before anything passes the EH?

Thank you for your time.
 
  • #15
bill alsept said:
Why is pressure required to keep the matter collapsing? Did you mean keep the matter FROM collapsing? If something becomes 100% dense (as I believe the singularity to be) and cannot get any denser then how can it collapse any farther? And why would it need pressure to keep it from collapsing?
Yes, I meant keep from collapsing, sorry. If you don't have outward pressure, the inward force of gravity will force the matter to collapse. And no, having the matter simply orbit doesn't work, as there are no stable orbits close to a black hole, let alone inside it.
 
  • #16
zhermes said:
Just to clarify, GR Is well behaved within the event horizon, its only near the singularity that it breaks down. In the case of a rotating or charged black hole, it can be a little worse.
While it is indeed true that General Relativity provides a sensible description of space-time inside the event horizon but outside the singularity, this doesn't mean we can trust it. In order to avoid the singularity, after all, General Relativity has to give an incorrect description of the black hole some distance outside that singularity. How far outside? We don't yet know. My expectation is that it may go as far as the event horizon, because the horizon itself forces quantum effects to have a significant impact on the behavior of the black hole. We think we understand the quantum behavior of the horizon itself. But that makes me doubt any of the non-quantum predictions of what goes on even just inside.
 
  • #17
I didn't understand the second part of your answer. What is orbiting? Basically I am asking how can something collapses after it has already collapsed as far as it can go.
 
  • #18
bill alsept said:
I didn't understand the second part of your answer. What is orbiting? Basically I am asking how can something collapses after it has already collapsed as far as it can go.
The only thing that sets how far it can collapse is the supporting pressure.
 
  • #19
I understand pressure is required to supports a balloons surface but not so simple on a bowling ball. Why is pressure needed on a complely solid object?
 
  • #20
bill alsept said:
I understand pressure is required to supports a balloons surface but not so simple on a bowling ball. Why is pressure needed on a complely solid object?
Well, consider a chunk of the matter. There will be a force inward caused by the gravitational attraction. If that force is not balanced by something, that force inward will cause the matter to accelerate inward. So if the matter is not collapsing, there must be a force outward to counterbalance the inward force of gravity. That force is a pressure.
 
  • #21
Chalnoth said:
While it is indeed true that General Relativity provides a sensible description of space-time inside the event horizon but outside the singularity, this doesn't mean we can trust it. In order to avoid the singularity, after all, General Relativity has to give an incorrect description of the black hole some distance outside that singularity. How far outside? We don't yet know.
That's a really good point. (My personal guess it much closer to the singularity ;)
 
  • #22
zhermes said:
That's a really good point. (My personal guess it much closer to the singularity ;)
For a slightly more detailed answer as to why I think it may need modification even just inside the event horizon, consider this.

From the point of view of the outside observer, an infalling object actually never crosses the event horizon. In fact, Hawking radiation causes the black hole to become smaller before the infalling object ever reaches it. So, what happens to the object if it is never allowed to even cross the event horizon?

Note that if we accept classical General Relativity, from the point of view of the infalling object, it does crash into the singularity in finite time. And this is also what happens even if the black hole is an evaporating black hole that has always existed. Last time I looked this up, however, nobody had managed to figure out what happens in a black hole that forms and evaporates in finite time with General Relativity.

Finally, consider that the Hawking Radiation encodes the information of whatever fell into the black hole, so that the radiation which leaves is physically connected to matter that entered into the black hole.

So my supposition is that the black hole can actually be seen as sort of a collision of matter occurring with an extreme amount of time dilation that is so destructive that it almost perfectly thermalizes any and all matter which enters the collision. This is, however, just supposition.
 
  • #23
Chalnoth said:
Well, consider a chunk of the matter. There will be a force inward caused by the gravitational attraction. If that force is not balanced by something, that force inward will cause the matter to accelerate inward. So if the matter is not collapsing, there must be a force outward to counterbalance the inward force of gravity. That force is a pressure.

Maybe the smallest particles in the universe only have space between them because they are each liberated and going through some repeated cycles of their own. When they are finally corralled and pushed together to the point they can no longer be liberated or move they loose any effect or phenomena they caused before. Could it even be possible that a black hole goes completely cold at the center? And would need no support again leading to the idea that the singularity may have a diameter instead of being a point?
 
  • #24
bill alsept said:
Maybe the smallest particles in the universe only have space between them because they are each liberated and going through some repeated cycles of their own. When they are finally corralled and pushed together to the point they can no longer be liberated or move they loose any effect or phenomena they caused before. Could it even be possible that a black hole goes completely cold at the center? And would need no support again leading to the idea that the singularity may have a diameter instead of being a point?
This is a real phenomena, and it happens inside white dwarfs and neutron stars. It's known as degeneracy pressure, because the fermions that make up these particles cannot occupy the same space at the same time. But this degeneracy pressure is limited, and eventually it is simply insufficient to keep these objects from collapsing inward. In the case of the white dwarf, it is the degeneracy pressure of the electrons in the atoms that make up the star. When that pressure gets too great, the electrons combine with the neutrons to form a neutron star. When the neutron degeneracy pressure of the neutron star is insufficient, it collapses to form a black hole. And no amount of pressure can prevent the collapse of the matter inside the event horizon.
 
  • #25
Sorry, I am not trying to beat a dead horse here but I am talking about after neutron degeneracy pressure of the neutron star and any other stages of collapse a body of mass may go through including the stage of converting to a black hole. Which I think is the same as all the other stages where the escape velocity just rises another notch. In this case it rises above the speed of light. But after that stage what stages are there and eventually you get to a particle that are so much smaller than anything else. There would be no other place to collapse to.
 
  • #26
bill alsept said:
Sorry, I am not trying to beat a dead horse here but I am talking about after neutron degeneracy pressure of the neutron star and any other stages of collapse a body of mass may go through including the stage of converting to a black hole. Which I think is the same as all the other stages where the escape velocity just rises another notch. In this case it rises above the speed of light. But after that stage what stages are there and eventually you get to a particle that are so much smaller than anything else. There would be no other place to collapse to.
Except that not all matter is fermionic. If the particles collapse to a bosonic state, then they can collapse as far as you like.
 
  • #27
Chalnoth what other matter is there besides fermions?
 
  • #28
Tanelorn said:
Chalnoth what other matter is there besides fermions?
At the very least, the photon, gluon, W and Z bosons, and the Higgs boson.
 
  • #29
Chalnoth said:
From the point of view of the outside observer, an infalling object actually never crosses the event horizon. In fact, Hawking radiation causes the black hole to become smaller before the infalling object ever reaches it. So, what happens to the object if it is never allowed to even cross the event horizon?
That's not an issue in GR. First, for all practical purposes the event horizon is going to increase is size from the newly accreted matter, not decrease in size---only the smallest of black-holes (with no known formation mechanism) decrease in size at all.
Second, the same argument would apply to the classic undergrad question 'how does the black-hole increase in mass at all?' --- which is a non-issue. The object crosses the event horizon without a problem, its just never observed.

Chalnoth said:
Note that if we accept classical General Relativity, from the point of view of the infalling object, it does crash into the singularity in finite time. And this is also what happens even if the black hole is an evaporating black hole that has always existed. Last time I looked this up, however, nobody had managed to figure out what happens in a black hole that forms and evaporates in finite time with General Relativity.
Yes, the singularity is of course an issue---but I don't see how adding a finite-aged black-hole complicates the issue. And note that you don't have evaporation with just general relativity.

Chalnoth said:
Finally, consider that the Hawking Radiation encodes the information of whatever fell into the black hole, so that the radiation which leaves is physically connected to matter that entered into the black hole.
Again, I don't see an issue here.

Chalnoth said:
So my supposition is that the black hole can actually be seen as sort of a collision of matter occurring with an extreme amount of time dilation that is so destructive that it almost perfectly thermalizes any and all matter which enters the collision. This is, however, just supposition.
I don't follow what you're saying.
 
  • #30
bill alsept said:
Sorry, I am not trying to beat a dead horse here but I am talking about after neutron degeneracy pressure of the neutron star and any other stages of collapse a body of mass may go through including the stage of converting to a black hole. ... But after that stage what stages are there and eventually you get to a particle that are so much smaller than anything else. There would be no other place to collapse to.
This is completely irrelevant as has already been stated many times. If you still don't understand, you should read a GR textbook. The nature of the material within the event horizon doesn't matter in general relativity. There is no such thing as 'a particle so much smaller than anything else'---you're argument is based on the premise that there is a fundamentally small thing, which cannot get smaller; you are then using that as an argument for the same point.
 
  • #31
zhermes said:
Yes, the singularity is of course an issue---but I don't see how adding a finite-aged black-hole complicates the issue. And note that you don't have evaporation with just general relativity.
The potential complication is that it is apparently unknown whether or not a singularity would form for a finite-aged black hole (in this case singularity simply meaning dense clump of matter at the center, instead of a mathematical singularity, since we'd be talking about a real black hole). That is, the time dilation may be so severe that the matter inside the event horizon just doesn't have enough time to collapse any significant amount before the black hole evaporates.

And yeah, obviously I was talking about a semi-classical black hole with regard to evaporation, which uses General Relativity to define the space-time but adds an evaporation mechanism.
 
  • #32
Chalnoth said:
The potential complication is that it is apparently unknown whether or not a singularity would form for a finite-aged black hole (in this case singularity simply meaning dense clump of matter at the center, instead of a mathematical singularity, since we'd be talking about a real black hole). That is, the time dilation may be so severe that the matter inside the event horizon just doesn't have enough time to collapse any significant amount before the black hole evaporates.
This is not an issue. Formation of black-holes and singularities has been thoroughly studied, by Papapetrou, Thorne, Penrose... Teukolsky I think. Again, in all astrophysically significant cases, evaporation can't occur----absorption of the CMB is far more rapid than the production of hawking radiation (and I can't recall for sure, but I think even very low ambient density environments, the bondi accretion is also more rapid than Hawking Radiation).
 
  • #33
zhermes said:
This is not an issue. Formation of black-holes and singularities has been thoroughly studied, by Papapetrou, Thorne, Penrose... Teukolsky I think.
Well, admittedly I haven't looked into this in great detail myself. But in this case I'm going off of my GR professor, Steve Carlip, who I think is generally quite good on this stuff. As far as I know, we're still a long way from really examining what GR has to say here for anything beyond the absolute simplest case. My understanding was that the only sort of black hole formation we could produce was due to symmetric infalling spherical shells, and that is a highly non-physical situation.

zhermes said:
Again, in all astrophysically significant cases, evaporation can't occur----absorption of the CMB is far more rapid than the production of hawking radiation (and I can't recall for sure, but I think even very low ambient density environments, the bondi accretion is also more rapid than Hawking Radiation).
Well, sure, but those accretion processes will all end in far, far less time than the expected black hole evaporation rate anyway. We're talking roughly [itex]10^{66}[/itex] to [itex]10^{100}[/itex] year timescales here. So I don't quite understand what this has to do with my point that we may not know much of anything about what's going on inside the black hole's event horizon.
 
  • #34
Chalnoth said:
At the very least, the photon, gluon, W and Z bosons, and the Higgs boson.

Chalnoth, are Bosons or force carriers conidered what is loosely called "ponderable matter". I am quite prepared to be wrong about this I just thought they werent.
 
  • #35
Tanelorn said:
Chalnoth, are Bosons or force carriers conidered what is loosely called "ponderable matter". I am quite prepared to be wrong about this I just thought they werent.
Well, they are either moving at the speed of light or are unstable. But when they are inside the event horizon of a black hole, moving at the speed of light doesn't prevent collapse, and the extreme space-time curvature may potentially make the W and Z bosons stable, in an analogous way to how the incredibly high pressure inside a neutron star makes neutrons stable.

Edit: Of course, this almost certainly isn't enough to produce a degenerate bosonic state at the center of a black hole, because you also have to get rid of the baryons, and baryon number is a conserved quantity in known physics. So we would probably need some beyond-standard-model interactions to get into a degenerate bosonic state, and that may open the door for still more bosons.
 
<h2>1. What is a black hole?</h2><p>A black hole is a region in space where the gravitational pull is so strong that nothing, including light, can escape from it. This is due to the extreme curvature of space-time caused by a large amount of mass being concentrated in a small area.</p><h2>2. What is the singularity in a black hole?</h2><p>The singularity is a point at the center of a black hole where the gravitational pull becomes infinite and the laws of physics as we know them break down. It is a point of infinite density and zero volume.</p><h2>3. What is the event horizon of a black hole?</h2><p>The event horizon is the boundary of a black hole where the escape velocity is equal to the speed of light. This means that anything that crosses the event horizon, including light, is unable to escape the gravitational pull of the black hole.</p><h2>4. What is the photon sphere of a black hole?</h2><p>The photon sphere is a region just outside the event horizon where photons (particles of light) can orbit the black hole. This is due to the extreme curvature of space-time, which causes the path of light to be bent back towards the black hole.</p><h2>5. Can we see the anatomy of a black hole?</h2><p>No, we cannot see the anatomy of a black hole directly because light cannot escape from it. However, we can observe the effects of a black hole on its surroundings, such as the distortion of light and the motion of stars and gas around it. This allows us to study and understand the anatomy of black holes indirectly.</p>

1. What is a black hole?

A black hole is a region in space where the gravitational pull is so strong that nothing, including light, can escape from it. This is due to the extreme curvature of space-time caused by a large amount of mass being concentrated in a small area.

2. What is the singularity in a black hole?

The singularity is a point at the center of a black hole where the gravitational pull becomes infinite and the laws of physics as we know them break down. It is a point of infinite density and zero volume.

3. What is the event horizon of a black hole?

The event horizon is the boundary of a black hole where the escape velocity is equal to the speed of light. This means that anything that crosses the event horizon, including light, is unable to escape the gravitational pull of the black hole.

4. What is the photon sphere of a black hole?

The photon sphere is a region just outside the event horizon where photons (particles of light) can orbit the black hole. This is due to the extreme curvature of space-time, which causes the path of light to be bent back towards the black hole.

5. Can we see the anatomy of a black hole?

No, we cannot see the anatomy of a black hole directly because light cannot escape from it. However, we can observe the effects of a black hole on its surroundings, such as the distortion of light and the motion of stars and gas around it. This allows us to study and understand the anatomy of black holes indirectly.

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