# Some questions on Blackholes

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I have read that Blackholes have properties Mass, Charge and Angular Momentum, and that the Event Horizon is the boundary between where spacetime is curved so much that all paths converge, and between where there are some paths that could diverge.

Putting aside Hawking Radiation, apparently "nothing?" can leave the EH.  As far as I understand, the "nothing" refers to anything with mass and any form of electromagnetism such as light, and perhaps categories of other things.

So if electromagnetic waves cannot exit the EH, how does the charge of the Blackhole create the electromagnetic effect that propagates around the black hole due to that charge?

Likewise with mass and curvature, how does the density of the mass "inside" the black hole's EH manage to curve the space time outside the EH, if the EH is a boundary where all paths converge?  If you were a bit mass under the EH, and you tried to emit your gravitational wave through the EH, that wave would have a geodesic that remains within the EH.  If that wave never exits the EH, and if ALL waves never exit the EH, what is causing the gravitational effect of the blackhole as experienced by objects outside the EH?

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This is because electromagnetic radiation is very different from an electrostatic field.

Likewise, gravitons, and also gravitational waves, are very different from a gravitational field.

Quantum field theory gives you a picture of this.

Can't happen.

Can happen.

Virtual particles can do... well, practically anything they want. In QFT lingo, virtual particles go as far as they want to go in the phase space. They can have mass, they can go faster than light, etc. As long as they disappear well within the domain of Heisenberg's uncertainty principle.

It's only external legs in Feynman diagrams that must behave.

Very good question, by the way.

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I would add a more simplistic elaboration to Joigus' Feynman diagram/virtual particle explanation.

The conserved quantities, mass, charge and ang momentum of a Black Hole ( classically ), as well as entropy ( classical/quantum hybrid ), which leads to temperature, and Hawking radiation, are all encoded in the Event Horizon.
No other feature of a Black Hole, other than the EH, are evidenced to the outside universe.

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17 hours ago, AbstractDreamer said:

So if electromagnetic waves cannot exit the EH, how does the charge of the Blackhole create the electromagnetic effect that propagates around the black hole due to that charge?

Once the gravitational collapse is complete, none of these quantities - charge, mass, angular momentum - are localisable, in particular not anywhere within or on the horizon. Instead, these quantities are now a global property of the entire spacetime, in the sense that they are encoded in the overall spacetime geometry. There’s nothing on or within the horizon that could possess these properties - Schwarzschild spacetime is entirely empty vacuum everywhere. Some features of the event horizon itself depend on these properties, but that does not imply that anything is actually located there.

Hence, nothing needs to propagate and escape, since there’s nothing there to escape from.

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So anything crossing into the EH joins/shares its charge, mass, angular momentum with the single entire entity of the blackhole?

Does a black hole experience gravitation from objects outside its EH? If some nearby spacetime is curved by some other object, does this curvature extend beyond the EH?  As a graviton wave crosses into the EH, does the black hole grow in energy?  Which if any of its properties will change?

If the black hole was of sufficient "volume? surface area?" where the external curvature at one location was significantly different from the other "side?", and taking the blackhole as a single non-quantisable entity, would this cause one part of the black hole to "move" in a different direction to another part of the black hole?  Would this cause pressure or stress within the black hole?

Edited by AbstractDreamer
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The Event Horizon is essentially a mathematical construct, however, it is also the manifestation of the space-time geometry.
As such, it is modified by properties like mass, charge and ang momentum ( in size shape and complexity  for lack of better descriptors ).
I don't quite understand the Beckenstein-Hawking mathematics, but it is a statistical mechanical interpretation of 'micro-states' of an EH ( as opposed to the previously believed single state of the 'no hair' theorem ) which leads to BH entropy.
( these micro states also arise in LQG, where they have a geometric interpretation )

As the EH is not an 'edge' to space-time, but rather a 'threshold', any curvature continues along with the global geometry through the threshold; BHs do experience gravity from external objects.

What is a 'graviton' wave ?
Gravitons are the supposed result of a quantum field theory of gravity.
Our current theory, GR, is classical; unless you are S Hawking, it is best not to mix the two.

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3 hours ago, MigL said:

As the EH is not an 'edge' to space-time, but rather a 'threshold', any curvature continues along with the global geometry through the threshold; BHs do experience gravity from external objects.

So "Schwarzschild spacetime is entirely empty vacuum everywhere", but Schwarzschild spacetime is not necessarily uniform or symmetrical?  For example a source of significant curvature on one side, external of the blackhole would create asymmetry of the spacetime beneath the EH?

So in a circumstance when spacetime is significantly asymmetric under the EH around the singularity, and when spacetime is significantly asymmetric above the EH around the black hole; would a non-rotating Schwarzschild blackhole still appear perfectly spherical?

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To give a very general answer - Schwarzschild spacetime relies on certain conditions that need to be in place for this particular geometry to arise. It is static, stationery, spherically symmetric, and asymptotically flat (ie there are no other distant sources of gravity). If any of these conditions is violated, we are no longer dealing with Schwarzschild spacetime, but something more complicated.

16 hours ago, AbstractDreamer said:

So anything crossing into the EH joins/shares its charge, mass, angular momentum with the single entire entity of the blackhole?

In principle, yes. But remember, a Schwarzschild BH is stationery and relies on an otherwise empty universe, meaning it doesn’t permit any changes - so you can’t have anything falling into it. If you add even as much as a single particle falling in, it’s no longer truly a Schwarzschild BH, but some other geometry.

16 hours ago, AbstractDreamer said:

Does a black hole experience gravitation from objects outside its EH? If some nearby spacetime is curved by some other object, does this curvature extend beyond the EH?

Yes and yes. But again, this wouldn’t be a Schwarzschild BH any longer.

16 hours ago, AbstractDreamer said:

As a graviton wave crosses into the EH, does the black hole grow in energy?  Which if any of its properties will change?

That’s a really good question! I presume you mean a gravitational wave. You can certainly embed a BH into a background gravitational wave field. The result would be something pretty complicated. I don’t know for sure just exactly what would happen, because, since GR is a non-linear theory, metrics don’t just add - you’d have to actually derive an entirely new solution for this scenario, which is likely only possible with numerical methods.

I can make an educated guess though - given the right wavelengths for your gravitational radiation, the event horizon of your BH would begin to oscillate and ‘vibrate’ (like a bell) and eventually achieve a state of resonance with the external wave field. But this also means that the BH itself becomes a source of gravitational radiation - so it would essentially reflect some of the radiation back out. I don’t know if it would re-radiate all of the energy, or absorb some of it and grow in mass; one would have to run the numbers to find out.

What’s more, the re-radiated waves will interfere with the incoming background waves in complicated non-linear ways, changing the wave field in ways that I can’t predict here now.

And to go even further - if you were to ‘turn off’ the external wave field somehow, the BH will slowly ‘ring down’ like a bell, and eventually become stationery; however, the surrounding spacetime will remain permanently altered by all these waves having gone through it. It’s called the gravitational memory effect.

This is a really complicated scenario, but very interesting.

16 hours ago, AbstractDreamer said:

If the black hole was of sufficient "volume? surface area?" where the external curvature at one location was significantly different from the other "side?", and taking the blackhole as a single non-quantisable entity, would this cause one part of the black hole to "move" in a different direction to another part of the black hole?

Yes, the event horizon will deform and ‘bulge out’ - this happens, for example, when two BH approach one another and merge.

16 hours ago, AbstractDreamer said:

Would this cause pressure or stress within the black hole?

No, because spacetime inside the horizon is empty (assuming no in-falling material), so there’s nothing there to experience stresses.

11 hours ago, AbstractDreamer said:

but Schwarzschild spacetime is not necessarily uniform or symmetrical?

Schwarzschild spacetime is always spherically symmetric. If it doesn’t have this symmetry, then it will be a different kind of geometry.

11 hours ago, AbstractDreamer said:

For example a source of significant curvature on one side, external of the blackhole would create asymmetry of the spacetime beneath the EH?

Yes.

11 hours ago, AbstractDreamer said:

So in a circumstance when spacetime is significantly asymmetric under the EH around the singularity, and when spacetime is significantly asymmetric above the EH around the black hole; would a non-rotating Schwarzschild blackhole still appear perfectly spherical?

No, it wouldn’t be spherical, and thus it wouldn’t be a Schwarzschild BH any longer. Schwarzschild geometry requires spherical symmetry.

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Thank you for such precise answers to my questions!  I shall digest them thoroughly.  My biggest enlightenment was learning that a Schwarzschild BH have very exact requirements... can I argue it is a physically improbable in our real universe -  to have a black hole that exists in perfectly flat, albeit possibly hyperbolic, spacetime?  Is it also true that flat Minkowski space is similarly improbable in our real universe?

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11 hours ago, AbstractDreamer said:

can I argue it is a physically improbable in our real universe

Yes, the precise Schwarzschild geometry will never occur in the real universe, because the necessary conditions aren’t given. However, there are many circumstances when it is a very useful approximation, and fits things quite closely.

11 hours ago, AbstractDreamer said:

Is it also true that flat Minkowski space is similarly improbable in our real universe?

The same answer here - while no region of real-world spacetime will ever be perfectly flat, there are many circumstances where this is very nearly the case, so it is again a very useful approximation to the real world. It all depends on the levels of accuracy you require for the problem at hand.

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• 5 months later...
On 9/13/2022 at 9:06 AM, Markus Hanke said:

I can make an educated guess though - given the right wavelengths for your gravitational radiation, the event horizon of your BH would begin to oscillate and ‘vibrate’ (like a bell) and eventually achieve a state of resonance with the external wave field. But this also means that the BH itself becomes a source of gravitational radiation - so it would essentially reflect some of the radiation back out. I don’t know if it would re-radiate all of the energy, or absorb some of it and grow in mass; one would have to run the numbers to find out.

What’s more, the re-radiated waves will interfere with the incoming background waves in complicated non-linear ways, changing the wave field in ways that I can’t predict here now.

And to go even further - if you were to ‘turn off’ the external wave field somehow, the BH will slowly ‘ring down’ like a bell, and eventually become stationery; however, the surrounding spacetime will remain permanently altered by all these waves having gone through it. It’s called the gravitational memory effect.

This is a really complicated scenario, but very interesting.

What kind of oscillation do you mean?   Do you mean a physical oscillation, that is, this EH boundary's location/position in space wobbles with some frequency?  Or do you mean oscillation in the values of a BH's properties, such as mass, angular momentum and charge?

If the position of the EH can "wobble", is it possible the wavelength of this is large enough to allow energy to escape?  For example if you were a photon just within the EH, but moving with 99.99999% of your speed directly away from the point of singularity, such that your geodesic is almost parallel with the EH boundary (you are still falling in just very very slowly).  If the boundary then wobbles sufficiently, is it possible to wobble "behind" you and momentarily wobble you outside the EH?   While it is likely you will wobble back within the EH on the next phase, is it possible to permanently leave the EH in this way?

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9 hours ago, AbstractDreamer said:

Do you mean a physical oscillation, that is, this EH boundary's location/position in space wobbles with some frequency?

No. What I mean is that the metric of spacetime itself becomes time-dependent here, in such a way that it appears to a far-away stationary observer as if the EH was oscillating with a quadrupole moment, even though the “position” of the horizon remains constant locally in a small neighbourhood. So what oscillates here is the relative separation between events, but not the coordinate position of the events themselves. This is somewhat similar to what’s called the “ring-down” phase at the end of a BH merger, where energy-momentum is dissipated away via gravitational radiation.

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