# What difference does it make if the Schwarzschild radii touch?

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If the mass of a BH is at the singularity what difference does it make if the Schwarzschild radii touch when they merge?

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Not all the mass is inside the Schwartzchild radius. Any spacetime region of higher gravitational potential has mass.

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If the mass of a BH is at the singularity what difference does it make if the Schwarzschild radii touch when they merge?

If you watch simulations of black hole mergers, you will see that the event horizons stretch out to each other as they approach.

If that didn't happen and the two event horizons just touched then the total mass would already be within the Schwarzschild radius of the combined mass (as rs is proportional to mass, you can demonstrate this with a simple drawing).

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Not all the mass is inside the Schwartzchild radius. Any spacetime region of higher gravitational potential has mass.

But does it matter if they touch when orbiting each other? If there is this mass in the spacetime region does it extend out beyond the event horizon as well then? What is so special about the Schwarzschild radius then?

How close can binary black holes get to each other before the ringdown starts? That is the question I'm trying to solve here.

Edited by Robittybob1
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But does it matter if they touch when orbiting each other? If there is this mass in the spacetime region does it extend out beyond the event horizon as well then? What is so special about the Schwarzschild radius then?

As soon as they touch the event horizon will become the size of the combined radii, so there will be one black hole, not two orbiting. (In reality it is more complex as they merge before then.)

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As soon as they touch the event horizon will become the size of the combined radii, so there will be one black hole, not two orbiting. (In reality it is more complex as they merge before then.)

the shape must change then. The two singularities will take time to travel the final "r" distance before there is just the one singularity, surely? (I think of this as the ringdown time).

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the shape must change then. The two singularities will take time to travel the final "r" distance before there is just the one singularity, surely? (I think of this as the ringdown time).

The singularities are irrelevant. We cannot know what they are doing (if they exist). We can only know what happens at the event horizon.

But, yes, as I said the shape changes.

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The singularities are irrelevant. We cannot know what they are doing (if they exist). We can only know what happens at the event horizon.

But, yes, as I said the shape changes.

Where is the mass of a black hole if it isn't at the singularity? Could you imagine a moving event horizon elongating? Could it be possible that it has the same volume but a different shape due to its speed when the BH is approaching the speed of light?

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Where is the mass of a black hole if it isn't at the singularity?

Inside (or maybe at) the event horizon. If we knew any more than that it would violate the "no hair" theorem.

Could you imagine a moving event horizon elongating?

Yes, because I have watched simulations of the merger of black holes.

Could it be possible that it has the same volume but a different shape due to its speed when the BH is approaching the speed of light?

Why would the speed change its shape?

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Robbity you are missing a key element of spacetime. Any positive energy/density region contains mass in the particles that surround a Schwartzchild region.

When the mass of a BH is provided they usually just refer to the mass that defines the Schwartzchild radius.

This does not include the spacetime regions prior to the event horizon such as the accretion disk, or the photon sphere.

If you look at a BH merger you can see an Einstein ring surrounding BOTH BH's. An Einstein ring is a special type of lensing due to the mass of the spacetime region itself. (That mass resides OUTSIDE the EH.

https://www.ligo.caltech.edu/video/ligo20160211v3

The only difference between spacetime and a solid is the density.

Spacetime has mass just like any solid object it's just far more spread out.

For example a void far removed from any gravitational structure has an average mass of 10-29 grams/m^3.

As you approach a gravitational body the average mass will steadily increased depending on the energy/density change as a function of radius and the changes in the stress/energy tensor.

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...

Yes, because I have watched simulations of the merger of black holes.

Why would the speed change its shape?

I saw those too, but that was more like linking rather than the elongation I was hoping for. You know how they say a particle flattens as it approaches the speed of light I thought the same effect but reversed could happen to a black hole. Could it flatten in the direction of motion? It is just a question.

Some relativistic effect like time dilation.

Robbity you are missing a key element of spacetime. Any positive energy/density region contains mass in the particles that surround a Schwartzchild region.

When the mass of a BH is provided they usually just refer to the mass that defines the Schwartzchild radius.

This does not include the spacetime regions prior to the event horizon such as the accretion disk, or the photon sphere.

If you look at a BH merger you can see an Einstein ring surrounding BOTH BH's. An Einstein ring is a special type of lensing due to the mass of the spacetime region itself. (That mass resides OUTSIDE the EH.

https://www.ligo.caltech.edu/video/ligo20160211v3

The only difference between spacetime and a solid is the density.

Spacetime has mass just like any solid object it's just far more spread out.

For example a void far removed from any gravitational structure has an average mass of 10-29 grams/m^3.

As you approach a gravitational body the average mass will steadily increased depending on the energy/density change as a function of radius and the changes in the stress/energy tensor.

You are right I don't think along those lines.

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You are right I don't think along those lines.

Behind the event horizon there is ZERO path for mass to escape.

A BH can only lose mass via Hawking radiation.

The mass radiated from a merger does NOT originate from behind the event horizon of either BH. As there is no spacetine path for mass to escape.

The mass loss is the spacetime regions Outside the event horizons.

Here is a good lengthy article on BH's outside the event horizon.

There is a tremendous amount of energy in the ergosphere and accretion disk. These regions can get far hotter than the center of any star.

http://arxiv.org/abs/1104.5499 :''Black hole Accretion Disk'' -Handy article on accretion disk measurements provides a technical compilation of measurements involving the disk itself

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I saw those too, but that was more like linking rather than the elongation I was hoping for. You know how they say a particle flattens as it approaches the speed of light I thought the same effect but reversed could happen to a black hole. Could it flatten in the direction of motion? It is just a question.

Some relativistic effect like time dilation.

As far as I know (which isn't much) the event horizon is invariant (i.e. it doesn't change with your relative velocity).

(... although that may not be true for observers in free fall towards it ...)

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As far as I know (which isn't much) the event horizon is invariant (i.e. it doesn't change with your relative velocity).

(... although that may not be true for observers in free fall towards it ...)

It would be one observer on one of the binary BHs looking across to the other. I've got no idea how we would apply relativity to that.

There was that guy David Waite who would sort out problems like that just for fun. He was on Physforum but Physforum is shut down for maintenance at the moment.

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Not all the mass is inside the Schwartzchild radius. Any spacetime region of higher gravitational potential has mass.

Robbity you are missing a key element of spacetime. Any positive energy/density region contains mass in the particles that surround a Schwartzchild region.

When the mass of a BH is provided they usually just refer to the mass that defines the Schwartzchild radius.

This does not include the spacetime regions prior to the event horizon such as the accretion disk, or the photon sphere.

.......

The only difference between spacetime and a solid is the density.

Spacetime has mass just like any solid object it's just far more spread out.

For example a void far removed from any gravitational structure has an average mass of 10-29 grams/m^3.

As you approach a gravitational body the average mass will steadily increased depending on the energy/density change as a function of radius and the changes in the stress/energy tensor.

I don't think using the Schwartzchild radius of a BH as a reference for gravitational potential is helpful here.

You may not intend this, but you seem to be suggesting that masses cause nearby spacetime ( and matter ) to have greater energy than distant spacetime ( and matter ) while the usual idea is that on average the mass-energy of matter etc is exactly or nearly equal to its negative gravitational mass-energy.

An analogy for the local high energy of an accretion disk would be an Apollo capsule flying through the atmosphere at 25000 knots after falling from the moon. Locally, a vast amount of kinetic energy seems to have been created from nothing; the simplest way to avoid this is to say that the capsule's increased kinetic energy is balanced by its decreased gravitational energy.

If a BH created a nearby positive energy/density region that energy would be absorbed by the BH causing exponential mass-energy creation.

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What's the definition of the Schwarzschild radius?

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You just have to look at the reference to see that there is a ton of mass in the accretion disk and ergoshere regions. How do you think accretion jets form?

Not all mass gets absorbed by the BH

For example equation 43 specifies mass density using $\rho$

What everyone seems to be missing is the fact that Nothing escapes the event horizon.

This includes mass, gravity waves can only be emitted from Outside the event horizons.

Edited by Mordred
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I think that, in regards to this question (and probably the other thread about gravitational waves) we can assume we are dealing with an idealised situation of two black holes with no significant amount of external material. (Unless Rob disagrees.)

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Regardless though nothing can ever exit the event horizons of either BH.

There is no spacetime path for mass to escape the event horizons in a BH merger. Even if those EH's are warped.

The mass radiated via gravity waves must originate from Outside the event horizons.

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What's the definition of the Schwarzschild radius?

Wikipedia:

The Schwarzschild radius (sometimes historically referred to as the gravitational radius) is the radius of a sphere such that, if all the mass of an object were to be compressed within that sphere, the escape velocity from the surface of the sphere would equal the speed of light.

Where does the mass of a BH reside?

The definition says it is a sphere. Did Schwarzschild ever envision a BH moving at half the speed of light? If gravity moves at the SoL but the singularity is moving at half the speed of light.

Wikipedia:

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Speed of light and speed of gravity are both invariant. The speed of the singularity won't change either the speed of light or gravity.

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Regardless though nothing can ever exit the event horizons of either BH.

There is no spacetime path for mass to escape the event horizons in a BH merger. Even if those EH's are warped.

The mass radiated via gravity waves must originate from Outside the event horizons.

Gravity gets out through the event horizon agreed? Do gravitons have mass? Does gravitational waves have energy hence a type of mass equivalence?

Are you using the word "warped" in the sense of the singularity no longer in the center of a sphere?

The mass radiated via gravity waves must originate from Outside the event horizons.

That is based on what research? (See if you can quote a paragraph that says something to that effect.)

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Where does the mass of a BH reside?

The definition says it is a sphere. Did Schwarzschild ever envision a BH moving at half the speed of light? If gravity moves at the SoL but the singularity is moving at half the speed of light.

These are addressed by basic tenets of relativity, which you're run across many times by now.

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No not really because it now appears that the event horizon which was used synonymously with the Sr is now no longer always a sphere.

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