What difference does it make if the Schwarzschild radii touch?

[Strange]

(To answer your question from the other thread: http://www.scienceforums.net/topic/94060-what-is-the-best-3d-description-of-gravitational-waves/?p=913986)

But don't discuss that further here!

[Carrock]

Here is the stress/energy tensor relations to the energy density and pressure.

 

[latex]T^{\mu\nu}=(\rho+p)U^{\mu}U^{\nu}+p\eta^{\mu\nu}[/latex]

 

 

what this equation means is that as the gravitational potential increases

 

So does the energy/mass density

Without analyzing this equation I agree with your conclusion.

I hope we agree that the gravitational potential distant from the BH is higher than it is near the BH.

 

I think the equation that may suit best on energy/density to curvature relations may be better seen here.

 

[latex]R_{ab}-\frac{1}{2}Rg_{ab}=8\pi GT_{ab}[/latex]

 

[latex]R_{ab}[/latex] is the ricci tensor,[latex] g_{ab}[/latex] is the curved by the presence of energy via the stress tensor [latex]T_{ab}[/latex]. G is the gravitational constant. R is the ricci scalar.

 

Conceptually this equation means curvature=energy...

Equation 1.1 the curvature equals energy statement is footnote 1.2.

 

http://www.google.ca/url?q=http://www.physics.usyd.edu.au/~luke/research/masters-geodesics.pdf&sa=U&ved=0ahUKEwj25uq8qOzLAhVM4WMKHWm4Ca0QFggRMAA&usg=AFQjCNEr4WEHhcvoL-LVhqBLVIcgBRFdkQ

From the above ref:

[This] statement says that the geometry of spacetime ..... is curved by the presence of energy.

'curvature=energy' is an oversimplification.

More precisely, curvature is caused by energy and a lesser amount of energy is associated with the curvature.

The negative gravitational P.E. near the BH ensures that there is lower energy density in that curved space than in distant 'flat' space.

 

 

 

 

 

Now as I understand the Schwartzchild metric it assumes the background vacuum =0. However I don't believe it states the curvature has zero energy/density.

Agreed. However due to the negative gravitational P.E. near a BH the curved space has a lower energy/density than distant space.

If gravitational P.E. is ignored it would have higher energy/density due to curvature.

 

I don't recall ever stating that energy is being created. Other than that your explanation is good. However you can see from the curvature statement I quoted from the wikilink that the curvature changes occur. If you look at the curvature to stress/tensor relations. You can see the curvature equates to energy momentum...

Via the stress/energy tensor. The formulas involved are posted in this thread.

 

You can see the first equation equates gravitational potential energy to the energy/density and pressure relations.

The second equation relates those relations to the curvature.

That's the part I think your missing.

Ignoring gravitational P.E. the energy density increases as you approach a BH.

I don't recall disputing this.

Including (negative) gravitational P.E. the energy density decreases as you approach a BH.

I don't think I'm missing anything.

 

I don't recall ever stating that energy is being created.

Sorry; I misunderstood.

 

Do we agree about negative gravitational P.E.?

[Mordred]

Ok I see what your getting at. This follows the convention that gravity potential energy is negative. This is really just a consequence of coordinate choice. Or rather the vector direction. In the next formula working from M to m.

 

By the classical Newtonian formula

 

[latex]U=-\frac{GMm}{r^3}[/latex]

 

However SR, or rather the Minkowskii looks at the vector change from at rest. With the equivalence principle. M_i=m_g.

 

The first equation I posted includes a term that specifies the coordinate choice.

 

[latex]T^{\mu\nu}=(\rho+p)U^{\mu}U^{\nu}+p\eta^{\mu\nu}[/latex]

 

 

[latex]\eta^{\mu\nu}[/latex] specifies Euclidean flat geometry.

Your covariant and contravarient terms specify your vector direction.

 

or more accurately the Minkoswkii form.

 

(Raised or lowered indices)

 

[latex]\mu\nu[/latex] being your tensor matrix coordinates

 

Essentially were both stating the same thing just under a different reference frame.

Were both right as their is no preferred coordinate frame of reference.

In Newtonian physics the relations are from center of mass outward.

 

In Minkowskii form it's at rest or Euclidean flat geometry as your coordinate baseline.

 

 

Now the other problem here is you you know mass has energy. You also know that when a particle gains kinetic energy it gains inertial mass.

 

So lets say you have 100 moles, of particles at a given volume lets use m^3.

Those particles have the same rest mass. Closer to the BH they gain inertial mass.

The negative gravitational P.E. near the BH ensures that there is lower energy density in that curved space than in distant 'flat' space.

 

 

Do we agree about negative gravitational P.E.?

Relative to reference frame M.

 

By this vector convention gravitational energy is negative. The gravitational binding energy is also negative.

 

so yes you have negative energy in a gravity well. By Newtonian convention.

(Thankfully GR uses the four momentum four velocity, and doesn't require potential energy).

Not that Newtonian theory works with gravity waves lol

Edited April 3, 2016 by Mordred

[Robittybob1]

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

This still seems to be a very good question if the words "Schwarzschild radius" is exchanged for the "event horizon"

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

The word "touch" needs to be more scientific too maybe we should say "overlap"

If the mass of a black hole is at the singularity what difference does it make if the event horizons overlap when black holes merge?

 

Did we find the answer?

 

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 r_s is proportional to mass, you can demonstrate this with a simple drawing).

Wouldn't the inertia of that mass have some bearing on this happening? Like two orbiting objects don't just fall toward each other.

You have to lose momentum to allow that to happen. It was a good point though. +1

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.

That is the big question that I see a lot of people are asking. How can we prove this?

Edited April 3, 2016 by Robittybob1

[Mordred]

No one will ever know. You can never measure beyond the event horizon.

 

No information escapes.

 

An outside observer cannot even see an object fall past the event horizon due to the amount of redshift.

Edited April 3, 2016 by Mordred

[Robittybob1]

No one will ever know. You can never measure beyond the event horizon.

 

No information escapes.

 

An outside observer cannot even see an object fall past the event horizon due to the amount of redshift.

Those accretion jets - you asked a question about them. Do they just involve surface effects?

[Mordred]

"A well-known feature of radial fall

towards the event horizon is that the coordinate time (the time that would be measured by a static distant observer) taken to reach the event horizon by a freely falling object is infinite(see e.g. [2]). This feature is accompanied by unlimited redshift:"

 

http://cosmology101.wikidot.com/local--files/main/touching_ghosts.pdf

Those accretion jets - you asked a question about them. Do they just involve surface effects?

They occur outside the event horizon.

[Robittybob1]

....

They occur outside the event horizon.

I didn't know that. There are plenty of drawings of accretion disks and polar jets but not much discussion. With the mass of the accretion disk close to a BH would that mass affect the shape of the event horizon? The accretion disc drawings seem enormous compared to the size of the BH. It seems surprising when we talk of the EHs touching when the accretion disks could be very significant too. I'll have to check the LIGO paper on GW150914 to see what they say about the accretion disks.

[Mordred]

Accretion jets and the reasons for them is a rather tricky subject. The leading theory for their cause afaik is the interaction with the BH,s magnetic field. Particularly in the ergosphere region.

 

Much like the vorticity of plasma in our sun creates magnetic fields so can infalling material from an accretion disk.

 

The process model usually involve Kerr rotating blackholes.

 

The various models is discussed in the accretion disk article I posted earlier this thread. One of the processes is the Penrose process or mechanism, the other is the Blandford-Znajek process.

 

(Hopefully I got the last process name correct lol)

 

Here is a non technical pop media coverage.

 

http://www.space.com/5285-powerful-black-hole-jet-explained.html

 

Part of the problem is that also theories that suggest part of the energy powering the jet isn't just from the disk itself, but may include the rotational energy of the BH.

 

Subject is still highly debated on that score.

 

Part of the latter also suggests an accretion disk via this angular momentum interaction can cause a rotating BH to lose some rotation.

Edited April 3, 2016 by Mordred

[Strange]

This still seems to be a very good question if the words "Schwarzschild radius" is exchanged for the "event horizon"

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

The word "touch" needs to be more scientific too maybe we should say "overlap"

If the mass of a black hole is at the singularity what difference does it make if the event horizons overlap when black holes merge?

 

No difference at all. How could it.

[Robittybob1]

 

No difference at all. How could it.

That was what I was thinking, but I'm sure Mordred wouldn't agree. I don't know enough to assist in this discussion, but it seems an interesting topic.

[Mordred]

Simply because the Event horizons could already be merged before the singularities merge. In this case you have no idea when the singularities merge. Due to the time dilation this event under this description would always be a future event.

 

Also the effects of the singularity merger behind an event horizon wouldn't escape the EH for us to record in the first place.

[Robittybob1]

Simply because the Event horizons could already be merged before the singularities merge. In this case you have no idea when the singularities merge. Due to the time dilation this event under this description would always be a future event.

 

Also the effects of the singularity merger behind an event horizon wouldn't escape the EH for us to record in the first place.

The ringdown wave pattern could be analysed. Important clues are there for those that know what to look for http://www.scienceforums.net/topic/94060-what-is-the-best-3d-description-of-gravitational-waves/?p=913986).

[Mordred]

In theory...I haven't yet seen any papers that suggest a measured analysis describing beyond the EH.

 

Have you?

Edited April 3, 2016 by Mordred

[Robittybob1]

In theory...I haven't yet seen any papers that suggest a measured analysis describing beyond the EH.

 

Have you?

Let me get this straight - the mass of a BH is beyond the event horizon isn't it? Its back to school for me if it isn't.

[Mordred]

Yes but we can't measure any change to the singularity mass. That information can only be inferred via the radius of the event horizon.

 

At the time the event horizon first formed. Though during a merger the radius of the EH would change this allows a more recent estimate of the singularity mass

Edited April 3, 2016 by Mordred

[Robittybob1]

Yes but we can't measure any change to the singularity mass. That information can only be inferred via the radius of the event horizon.

 

At the time the event horizon first formed. Though during a merger the radius of the EH would change this allows a more recent estimate of the singularity mass

What! I thought the EH was calculated from the mass via the Schwarzschild radius formula. How is one going to see the radius of the event horizon otherwise. Have I missed something? What were the steps?

[As an aside: with all the discussion on the BH we've been having I can read the papers put out by LIGO Team and just about know what they mean now. Thanks for the help Mordred and Strange and others of course, but you two in particular.]

[Strange]

Yes but we can't measure any change to the singularity mass.

 

If there is any such thing as a singularity.

[Mordred]

 

If there is any such thing as a singularity.

That's the other question lol. I lost track of the number of theories of what lies beyond an EH.

 

Infinite density,

Wormhole tunnels to new universe

Wormhole tunnels joining multiple Bhs

Solid core,

 

 

The list goes on and on.

[Strange]

Fuzzball

[Robittybob1]

 

If there is any such thing as a singularity.

But there is a mass beyond the EH. But I'm not sure that BH mass has gravity for that would be information coming through the EH. But wasn't that the whole point of BHs they had mass and gravity.

Can we say there is mass beyond the EH? It is not important whether it is at a singularity.

[Mordred]

What! I thought the EH was calculated from the mass via the Schwarzschild radius formula. How is one going to see the radius of the event horizon otherwise. Have I missed something? What were the steps?

 

Can you see an event horizon?

 

We can only measure the gravitational influence. We never never see the EH. The gravitational influence is the curvature outside the EH.

That curvature changes regardless of whether or not we can see it's change.

 

For example on Earth we are a static observer. We wouldn't see the change. However if your an infalling observer you can record the change.

 

For example if a BH is removed from any other object. Outside of gravitational influence, to any other object and has no unfailing material.

 

You would have no means of even knowing it's there.

The surrounding curvature would still be affected. The curvature will change regardless of the observer.

However we may or may not be able to directly measure that change depending on observer limits.

 

We can get around this by observing how other objects react to the curvature.

 

This is why it's correct to state the information of the BH's mass is contained in the spacetime region outside the event horizon.

 

Gravity being curvature and the rate of curvature change being maximum c.

Edited April 3, 2016 by Mordred

[Robittybob1]

Can you see an event horizon?

 

We can only measure the gravitational influence. We never never see the EH. The gravitational influence is the curvature outside the EH.

That curvature changes regardless of whether or not we can see it's change.

 

For example on Earth we are a static observer. We wouldn't see the change. However if your an infalling observer you can record the change.

 

For example if a BH is removed from any other object. Outside of gravitational influence, to any other object and has no unfailing material.

 

You would no means of even knowing it's there.

The surrounding curvature would still be affected. The curvature will change regardless of the observer.

That is a bit different to the situation you were talking about in http://www.scienceforums.net/topic/94222-what-difference-does-it-make-if-the-schwarzschild-radii-touch/page-6#entry914745 where there was a merger and a change in the mass.

Edited April 3, 2016 by Robittybob1

[Mordred]

Yes and no if you think about observer limitation. An outside observer would never see the event horizon change.

At one time blackholes were called "frozen stars" that terminology dropped out of literature.

Edited April 3, 2016 by Mordred

[Robittybob1]

Yes and no if you think about observer limitation.

The LIGO team only had the trace to go from. From that they made list of deductions. So is that the type of observer you are talking about? I don't follow the going into a BH concepts very well.

Just confirm for me please: a BH has mass beyond the EH and that mass produces/has gravity?

Edited April 3, 2016 by Robittybob1