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### Author Topic: What energy does a particle have at the event horizon of a Schwarzschild BH?  (Read 8440 times)

#### itisus

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##### What energy does a particle have at the event horizon of a Schwarzschild BH?
« on: 01/12/2009 18:44:39 »
Suppose a particle with mass m falls radially from rest in flat space to the event horizon of a Schwarzschild black hole without losing anything to radiation.  How much energy (mass) does it contribute?  Obviously it is not infinite, despite the common assertion that it reaches the speed of light. So presumably it either becomes massless or enters at less than c.  I'm assuming it actually does pass the horizon, although that can't be verified by direct observation.

#### Mr. Scientist

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##### What energy does a particle have at the event horizon of a Schwarzschild BH?
« Reply #1 on: 01/12/2009 22:31:16 »
Suppose a particle with mass m falls radially from rest in flat space to the event horizon of a Schwarzschild black hole without losing anything to radiation.  How much energy (mass) does it contribute?  Obviously it is not infinite, despite the common assertion that it reaches the speed of light. So presumably it either becomes massless or enters at less than c.  I'm assuming it actually does pass the horizon, although that can't be verified by direct observation.

It doesn't add anything, simply because there is no information loss. The particles after passing the event horizon will immediately tunnel back into the vacuum.

#### graham.d

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##### What energy does a particle have at the event horizon of a Schwarzschild BH?
« Reply #2 on: 02/12/2009 08:58:56 »

It doesn't add anything, simply because there is no information loss. The particles after passing the event horizon will immediately tunnel back into the vacuum.

That is an unusual view (unless referring to Hawking radiation, but that is not what the question is about) and not one I've come across except, perhaps, as highly speculative ideas regarding a BH being a wormhole to a WH. Have you any reference that supports this hypothesis?

The (Schwarzschild) EH of a BH is really only defined from infinity or, at least, a long way off. A mass would only attain a theoretical infinite value if falling from that distance. A mass sufficiently close to what we, at a great distance see as a BH, may not see a BH at all. Local mass can be collected by a BH in order to form it but mass falling from a distance, such that an observer close to the mass could see the BH Event Horizon, would see the mass approach the EH, but Time Dilation and Doppler shift would result in the mass never crossing the EH from the observer's perspective. The nasty infinity is effectively cosmically censored :-)

#### Mr. Scientist

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##### What energy does a particle have at the event horizon of a Schwarzschild BH?
« Reply #3 on: 02/12/2009 09:25:33 »

It doesn't add anything, simply because there is no information loss. The particles after passing the event horizon will immediately tunnel back into the vacuum.

That is an unusual view (unless referring to Hawking radiation, but that is not what the question is about) and not one I've come across except, perhaps, as highly speculative ideas regarding a BH being a wormhole to a WH. Have you any reference that supports this hypothesis?

The (Schwarzschild) EH of a BH is really only defined from infinity or, at least, a long way off. A mass would only attain a theoretical infinite value if falling from that distance. A mass sufficiently close to what we, at a great distance see as a BH, may not see a BH at all. Local mass can be collected by a BH in order to form it but mass falling from a distance, such that an observer close to the mass could see the BH Event Horizon, would see the mass approach the EH, but Time Dilation and Doppler shift would result in the mass never crossing the EH from the observer's perspective. The nasty infinity is effectively cosmically censored :-)

Of course:

http://www.newscientist.com/article/dn6151-hawking-cracks-black-hole-paradox.html

I would never mislead anyone.

#### Mr. Scientist

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##### What energy does a particle have at the event horizon of a Schwarzschild BH?
« Reply #4 on: 02/12/2009 09:27:34 »
And hopefully, as you will see, it does refer to the OP:

''Suppose a particle with mass m falls radially from rest in flat space to the event horizon of a Schwarzschild black hole without losing anything to radiation.  How much energy (mass) does it contribute?''

Hence there is no point considering sytems which have fallen into black holes. They won't stay there long.

#### graham.d

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##### What energy does a particle have at the event horizon of a Schwarzschild BH?
« Reply #5 on: 02/12/2009 12:36:16 »
Thanks for the reference, however this does not say that the mass falling into a BH will not stay there long. The article, which I'm sure is much simplified, refers to information not being lost and being recovered when the BH evaporates. The information loss is in conflict with QM. I don't think Hawking has changed his views regarding how long the evaporation takes and that it is only very small ones that do so in short time.

I think the question is about why a mass going into a BH is not infinite at the EH. A good question, but it need not invoke QM to answer. It does involve General Relativity for a thorough answer, though I hoped my qualitative argument was adequate.

#### Mr. Scientist

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##### What energy does a particle have at the event horizon of a Schwarzschild BH?
« Reply #6 on: 02/12/2009 12:54:05 »
Well it wouldn't stay long. The ''pressure'' of it being information of this universe assures me as a scientifically-minded person that the tunnelling process should be quite quick to near-instantaneous.

#### graham.d

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##### What energy does a particle have at the event horizon of a Schwarzschild BH?
« Reply #7 on: 02/12/2009 17:29:20 »
Re-reading what I said previously, I gave the impression that the mass would not cross the EH, but it will if on a perfect trajectory. It is just that you can't see it cross. The mass (and diameter) of the BH will increase accordingly, and this should include the mass due to object's velocity also. If the mass originates from a position from which you can observe an EH then I can't see why this would not correspond to an infinite mass gain for the BH either, as observed from the starting point. As I said, good question. Perhaps someone else has a view.

Mr S, If BH's exist, which is not certain though evidence points that they do, then mass must have got in there and not immediately "tunneled" out by some means. I could not find any paper that describes the phenomena you postulate. If you can point to some reputable journal where this is described I would be most interested.

#### yor_on

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##### What energy does a particle have at the event horizon of a Schwarzschild BH?
« Reply #8 on: 02/12/2009 19:37:38 »
Suppose a particle with mass m falls radially from rest in flat space to the event horizon of a Schwarzschild black hole without losing anything to radiation.  How much energy (mass) does it contribute?  Obviously it is not infinite, despite the common assertion that it reaches the speed of light. So presumably it either becomes massless or enters at less than c.  I'm assuming it actually does pass the horizon, although that can't be verified by direct observation.

As you say mass can never reach 'c' inside our universe so the speed it will have must be under that. As for the momentum, the same applies, it will have a 'count able' amount.

What happens after it is lost to our universes observation? Inside the EV?
Some argue that it never will reach past the EV. If that is true then it seems that all BH are 'constructed' at the BB.

But if you see it as possible to pass the EV inside our universes timeframe then that mass will at some point become part of a 'singularity' which in fact should mean that all particles falling past the EV at some point becomes 'uncountable' and therefore 'infinite mass'

---

I'm sort of joking there btw.
Anything 'infinite mass or energy if you like' is no longer a part of SpaceTime.
« Last Edit: 02/12/2009 19:39:23 by yor_on »

#### itisus

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##### What energy does a particle have at the event horizon of a Schwarzschild BH?
« Reply #9 on: 04/12/2009 03:57:36 »
Well, I'll try again.  The fact that we never see anything cross the EH is irrelevant.  Use isotropic coordinates and it crosses.

I don't care how long it stays.

I'm just asking how much mass/energy it adds to the BH.  Assuming there are large black holes -- which is reasonably well confirmed by observation -- they must have accreted their mass/energy from stuff crossing the horizon.  Their mass/energy is neither zero nor infinity.  Therefore a particle crossing the EH must contribute some particular (within Heisenberg limits) energy.  Someone must know how to compute it, hopefully someone here.  I don't, and sure would like to find out.

#### Mr. Scientist

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##### What energy does a particle have at the event horizon of a Schwarzschild BH?
« Reply #10 on: 04/12/2009 08:18:20 »
Re-reading what I said previously, I gave the impression that the mass would not cross the EH, but it will if on a perfect trajectory. It is just that you can't see it cross. The mass (and diameter) of the BH will increase accordingly, and this should include the mass due to object's velocity also. If the mass originates from a position from which you can observe an EH then I can't see why this would not correspond to an infinite mass gain for the BH either, as observed from the starting point. As I said, good question. Perhaps someone else has a view.

Mr S, If BH's exist, which is not certain though evidence points that they do, then mass must have got in there and not immediately "tunneled" out by some means. I could not find any paper that describes the phenomena you postulate. If you can point to some reputable journal where this is described I would be most interested.

I will certainly find one... its a question that can be answered however in the existence of a white hole. To very production of a black hole there may in act be a black hole pair-creation. In fact i once speculated that if black holes and white holes can be created in a pair production, it may be able to feed of the white holes mass long enough to reach a larger body, and grow slowely as it gobbled its matter.

BUT!!! as you have amply said, this is all theory. I would like to believe black holes exist, but we surely need more evidence to make any absolutions on anything about them... but i do hope you regard my contribution above as the ''scientific'' explantion, and not itself an absolution.

Cheers

#### Mr. Scientist

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##### What energy does a particle have at the event horizon of a Schwarzschild BH?
« Reply #11 on: 04/12/2009 08:22:26 »
Well, I'll try again.  The fact that we never see anything cross the EH is irrelevant.  Use isotropic coordinates and it crosses.

I don't care how long it stays.

I'm just asking how much mass/energy it adds to the BH.  Assuming there are large black holes -- which is reasonably well confirmed by observation -- they must have accreted their mass/energy from stuff crossing the horizon.  Their mass/energy is neither zero nor infinity.  Therefore a particle crossing the EH must contribute some particular (within Heisenberg limits) energy.  Someone must know how to compute it, hopefully someone here.  I don't, and sure would like to find out.

How much mass would it add... It's not longer part of our universe if that be the case, and black holes are not closed systems internally. Then of course there is the speed at which the particle is moving at, then there is the mass of the black hole in question as well.

#### graham.d

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##### What energy does a particle have at the event horizon of a Schwarzschild BH?
« Reply #12 on: 04/12/2009 13:50:28 »
itisus, your question is a good one and I don't know the answer. It may well be that nobody does exactly but I expect there are a lot of theories. It is not certain what is meant by mass itself (gravitational or inertial) or how much the mass of a body we observe is actually the energy of the gravitational scalar field. I think the easiest way to think about this is to consider only a two body problem of an object and a non-rotating black hole. An inert observer being permitted.

Let's suppose the observer is positioned a long way off but perpendicular to a line drawn between the BH and the object. Let's also suppose the BH and object somehow start off stationary with respect to each other and the observer. There will be a potential energy between the object and the BH and, as the two are drawn to each other this will translate into kinetic energy. Both object and, to a much lesser extent, the BH will accelerate towards each other. Eventually the object will disappear into the EH of the BH and, by conservation of momentum, the resulting object will again be stationary. The total energy of the system will be the same, so the BH will grow, as viewed by the observer, according to the energy gained by the impact of the object. This will be the sum of it's stationary mass and of the mass due to the velocity at impact of the object. The energy gain should be the same as calculated from the initial potential energy.

Whether it is fair to make the simplifications here is open to conjecture. Some theories, probably the most accepted ones, have mass as only having meaning with respect to the total mass in the universe, so extrapolating to a two body system, and one that ends up as one body, as in this case, may not be valid. Also the position of the observer should not matter, but I'm not wholly convinced that this is the case here; I think it's OK but the situation can get very complex.

The point you make about getting an infinite energy situation seems a tricky problem. If the object was positioned initially a similar distance from the BH as the observer, then a second observer on the object would also perceive the BH as having an EH. The consequence of this is that when he falls through it he will, as seen by the first observer, to have infinite energy. However this seems in contradiction to the finite potential energy at which the two objects start off.

I think I may be missing something obvious. Maybe someone on the NS team knows, or at least knows someone who does???

#### itisus

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##### What energy does a particle have at the event horizon of a Schwarzschild BH?
« Reply #13 on: 09/12/2009 02:44:11 »
itisus, your question is a good one and I don't know the answer. It may well be that nobody does exactly but I expect there are a lot of theories. It is not certain what is meant by mass itself (gravitational or inertial) or how much the mass of a body we observe is actually the energy of the gravitational scalar field. I think the easiest way to think about this is to consider only a two body problem of an object and a non-rotating black hole. An inert observer being permitted.

.... However this seems in contradiction to the finite potential energy at which the two objects start off.

Yes, I had no idea this was so complex.  I just noticed that black holes must accrete mass/energy if they exist, and it looked like the energy could be calculated by someone with a bit more skill than mine.  It seemed like an obvious question and there must be an answer.

Is it any easier to find the event horizon energy of a radial photon that begins at infinity with a very low frequency?  I suspect not, but it gets rid of mass and velocity problems.

#### itisus

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##### What energy does a particle have at the event horizon of a Schwarzschild BH?
« Reply #14 on: 09/12/2009 03:13:19 »
How much mass would it add... It's not longer part of our universe if that be the case, and black holes are not closed systems internally. Then of course there is the speed at which the particle is moving at, then there is the mass of the black hole in question as well.
What do you mean by "not closed systems internally"?
By "not longer part of our universe," I assume you mean it is behind the horizon.  But it's mass, rotation, and charge are still available.  I hope entropy is not relevant here.

#### itisus

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##### What energy does a particle have at the event horizon of a Schwarzschild BH?
« Reply #15 on: 10/12/2009 01:31:58 »
I had thought the horizon was just an artifact of the external observer viewpoint, but it is indeed real.  Now I just think the solution is wrong, but I agree that nothing crosses the horizon.  And my original question about how much energy a particle delivers to the BH is still unanswered.

« Last Edit: 01/02/2010 06:57:51 by itisus »

#### Mr. Scientist

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##### What energy does a particle have at the event horizon of a Schwarzschild BH?
« Reply #16 on: 10/12/2009 14:11:51 »
How much mass would it add... It's not longer part of our universe if that be the case, and black holes are not closed systems internally. Then of course there is the speed at which the particle is moving at, then there is the mass of the black hole in question as well.
What do you mean by "not closed systems internally"?
By "not longer part of our universe," I assume you mean it is behind the horizon.  But it's mass, rotation, and charge are still available.  I hope entropy is not relevant here.

They have topological openings.

#### graham.d

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##### What energy does a particle have at the event horizon of a Schwarzschild BH?
« Reply #17 on: 10/12/2009 16:33:55 »
Do you mean "Wormholes" Mr S? It would be clearer to say this. In a more general sense all openings (geometrically) are topological.

#### yor_on

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##### What energy does a particle have at the event horizon of a Schwarzschild BH?
« Reply #18 on: 12/12/2009 18:47:55 »
Reading you I get confused, an easy thing to achieve I freely admit. Outside an EV or EH as some say our universes laws exist, with their limits. Inside we find no known laws. As soon as you pass the EV you are no longer a part of this universe, and that's the truth as far as I know.

And invariant mass (matter) will be the part of an object that always stays the same, no matter it's apparent weight, so mass is easily defined as I see it, no matter what 'system' you use.

The real question itisus is whether anything can pass the Event horizon. If it can't this discussion is irrelevant. If it can then it will at some part of its travel transform into a limitless mass-energy.

#### jartza

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##### What energy does a particle have at the event horizon of a Schwarzschild BH?
« Reply #19 on: 09/12/2010 15:54:41 »
You guys seem to be having a little bit of a problem here. Well let me help:

When mass m falls into a black hole the mass increase of the black hole is m !!

Those drawings have nothing to do with this. It's just some forum bug.
- Is that better? - Mod.  (Irrelevant drawings removed)
« Last Edit: 09/12/2010 16:25:45 by peppercorn »

#### jartza

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##### What energy does a particle have at the event horizon of a Schwarzschild BH?
« Reply #20 on: 09/12/2010 21:15:32 »
Yes, thank you for removing gravity transformer blueprints

It's really simple to calculate the mass increase of black hole when mass m is dropped from height h into the black hole. It's m.

#### granpa

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##### What energy does a particle have at the event horizon of a Schwarzschild BH?
« Reply #21 on: 10/12/2010 19:25:34 »
time dilation at the event horizon is total yet the gravity there is not infinite.

for a photon to leave the event horizon it would have to have an infinite frequency because as it left it would become infinitely redshifted.

this is purely a time dilation effect.

but of course, because of this time dilation, photons neither reach nor leave the event horizon.

hence no need for infinities.

this is the answer to the op.

I'm sure people will reply that this is non-physical and from the photons point of view nothing special happens at the event horizon.
I understand this perfectly well but I will leave it to them to explain it to the op.

if that was unclear then look at it this way.

imagine that it was an infinite distance to the horizon.
nothing will ever reach or leave the horizon.
but that doesnt mean that gravity necessarily imparts an infinite amount of energy to anything falling in.
it just means that nothing will or ever could ever reach the horizon in the first place.

infinite time dilation does not = infinite gravitational energy
« Last Edit: 10/12/2010 19:35:14 by granpa »

#### jartza

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##### What energy does a particle have at the event horizon of a Schwarzschild BH?
« Reply #22 on: 12/12/2010 02:55:06 »
I confirm what granpa said!

When mass m is dropped from height h into a black hole, mass m is added to the black hole.
BUT seen from higher height, m was smaller, and mass increase was smaller!

#### jartza

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##### What energy does a particle have at the event horizon of a Schwarzschild BH?
« Reply #23 on: 14/12/2010 00:05:17 »
But if you are hanging on the event horizon, not falling, you will say that the stuff that is falling from above has infinite energy.

When an object with infinite energy has fallen past you into the black hole, you will say that an infinite increase of black hole's mass occurred when the object with infinite mass plunged there.

#### JP

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##### What energy does a particle have at the event horizon of a Schwarzschild BH?
« Reply #24 on: 14/12/2010 04:45:57 »
But if you are hanging on the event horizon, not falling, you will say that the stuff that is falling from above has infinite energy.

When an object with infinite energy has fallen past you into the black hole, you will say that an infinite increase of black hole's mass occurred when the object with infinite mass plunged there.

I think this is mistaken.  Generally when you consider different reference frames you need to work with the stress-energy tensor rather than just mass/energy.  I think the black hole probably gains mass equivalent to the mass of the object if it were resting in a flat region of space-time far from the black hole...

Here's an example of why you can't just think of mass/energy:  Assume you do a calculation that says if the mass of a spaceship is high enough, it will form a black hole.  I build this spaceship, but it doesn't have enough mass.  I then get into it and fly by you at 0.999999 c.  You see it now as having a huge amount of energy--enough, you say, to form a black hole.  Of course it doesn't form a black hole, since to me, sitting on board the spaceship, the mass of it hasn't changed!  The problem is that we're in two different reference frames and I'm pretty sure that the thing that tells you if you form a black hole is only mass/energy if the object is at rest with respect to you.  If the object is moving, you need to account for its momentum, which comes in through the stress-energy tensor.

Also, infinite energy isn't an issue here, since the infalling matter isn't moving at the speed of light in any reference frame.

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##### What energy does a particle have at the event horizon of a Schwarzschild BH?
« Reply #24 on: 14/12/2010 04:45:57 »

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