What difference does it make if the Schwarzschild radii touch?

[Robittybob1]

 

Centre of mass is not the same thing as a singularity. Those equations are for any orbiting pair of bodies, such as the Earth and Sun (as I think it says). Those do not have singularities at the centre. You can treat the mass of any spherically symmetrical object as if it were entirely concentrated at the centre. Even if it were entirely at the surface.

 

It is a distance from the centre.

If we took a 30 solar mass BH and worked out its Sr from that radius we could work out the surface area, and divide the kgs by the square meters so we'd get its kg/m^2 value. Has that mass per square meter got a density? Does it have a depth?

[Mordred]

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

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.

Without going into energy being a property lets avoid gravitons and use gravitational field energy.

 

 

(Of course we could get into Komar,Bondi and ADM mass but I don't we really need to.) As it would be off the OP topic

 

https://en.m.wikipedia.org/wiki/Mass_in_general_relativity

Edited April 1, 2016 by Mordred

[Robittybob1]

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

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.

Without going into energy being a property lets avoid gravitons and use gravitational field energy.

 

 

(Of course we could get into Komar,Bondi and ADM mass but I don't we really need to.) As it would be off the OP topic

 

https://en.m.wikipedia.org/wiki/Mass_in_general_relativity

Was that an answer to my question #51?

[Mordred]

No it was related to Imaatsfal's post

 

Though it does relate to how energy of a binary system can radiate prior to the event horizons meeting.

Edited April 1, 2016 by Mordred

[swansont]

If we took a 30 solar mass BH and worked out its Sr from that radius we could work out the surface area, and divide the kgs by the square meters so we'd get its kg/m^2 value. Has that mass per square meter got a density? Does it have a depth?

 

 

The first question is a combination of "no" and "this makes no sense, please go and learn what density is (along with other basic concepts)"

 

The second is "no, it's a surface"

[Robittybob1]

 

 

The first question is a combination of "no" and "this makes no sense, please go and learn what density is (along with other basic concepts)"

 

The second is "no, it's a surface"

Could you direct me to a paper that explains the current thinking of what a black hole is like please? I find your answers really confusing. We must be talking about completely different things.

[swansont]

Could you direct me to a paper that explains the current thinking of what a black hole is like please? I find your answers really confusing. We must be talking about completely different things.

 

 

That's not how the literature works, unless someone has written a summary article somewhere. It's not my field, so I don't know. Do you know how to Google?

 

My answers might be less confusing if you bothered to learn the basic material that these discussions rely on. For example, Strange answered your question about whether the event horizon has a depth, but since he phrased it a certain way you obviously missed that he was giving you the information you need, you missed it and immediately asked the same question again. It's the distance from the center — it's a surface. Mathematical surfaces have no thickness. The are two-dimensional. You even acknowledge this when you do a surface density — you get kg/m^2. The units tell you that there are only two dimensions, so there can't be a thickness. But you are apparently oblivious to all of this, because you ask a question that by all rights, you should already know the answer to if you're going to try and decipher the more advanced material.

 

Learn the basics. This got old some time ago. Discussions about black holes (or any advanced topic) should not include repeated remedial math and/or physics lessons.

[Strange]

Could you direct me to a paper that explains the current thinking of what a black hole is like please? I find your answers really confusing. We must be talking about completely different things.

https://en.wikipedia.org/wiki/Black_hole

 

With your questions about the event horizon, you seem to be thinking it is made of something. It isn't. It is just a location (where the interior is not causally connected to the exterior).

 

Can you be more specific about what you find confusing?

[Robittybob1]

https://en.wikipedia.org/wiki/Black_hole

 

With your questions about the event horizon, you seem to be thinking it is made of something. It isn't. It is just a location (where the interior is not causally connected to the exterior).

 

Can you be more specific about what you find confusing?

I have just done the calculations I was suggesting above and I am surprised by the answer.

I looked at 3 BHs Mass1 = 36, Mass2 = 29 and Mass final = 62 (solar masses)

 

These are the masses in kg 7.16E+31, 5.77E+31, 1.23E+32

 

 

 

And their Schwarzschild radii 1.06E+05 8.55E+04 1.83E+05

area of sphere with this radius: 1.33E+06 1.08E+06 2.30E+06

 

then I worked out how much mass each BH had for every m^2 of area of the event horizon and they were all the same!

mass/m^2 5.3655E+25 5.3655E+25 5.3655E+25

 

 

Mass of Earth 5.972 × 10^24 So for each square meter of the event horizon the BHs have 8.98 times the mass of the Earth.

 

Have I done my calculations wrong?

 

 

I see the error I didn't use r^2 in my area calculations

area of sphere with this radius: 1.42E+11 9.20E+10 4.20E+11

then I worked out how much mass each BH had for every m^2 of area of the event horizon: 5.0524E+20, 6.2719E+20, 2.9336E+20

So for each square meter of the event horizon the BHs have: 8.46E-05, 1.05E-04, 4.91E-05 Earth masses

 

Where is this mass WRT the BH? Is it at/near the singularity?

Edited April 1, 2016 by Robittybob1

[Strange]

That can't be right. The Schwarzschild radius is proportional to mass, so the area is proportional to mass². Dividing mass by that is going to give you some constant / mass.

 

 

So for each square meter of the event horizon the BHs have: 8.46E-05, 1.05E-04, 4.91E-05 Earth masses

 

What is the relevance of mass/area ?

 

Where is this mass WRT the BH? Is it at/near the singularity?

 

You don't and can't know. It doesn't make any difference.

 

It could all be at the singularity. It could all be at the event horizon. It could be evenly distributed inside.

 

You don't and can't know. It doesn't make any difference.

Edited April 1, 2016 by Strange

[Robittybob1]

That can't be right. The Schwarzschild radius is proportional to mass, so the area is proportional to mass². Dividing mass by that is going to give you some constant / mass.

 

 

What is the relevance of mass/area ?

I want to know where that mass is in relation to that area.

[Strange]

I want to know where that mass is in relation to that area.

 

And how is dividing mass by area going to help?

[swansont]

 

You don't and can't know. It doesn't make any difference.

 

It could all be at the singularity. IKt could all be at the event horizon. It could be evenly distributed inside.

 

You don't and can't know. It doesn't make any difference.

 

 

deja vu. It's like I've seen this answer before.

[imatfaal]

What is the relevance of mass/area ?

 

[tongue in check & devil's advocate]

 

Weellll... before it goes into the black hole there is an entropy involved in this matter which makes up the mass and after it goes through the event horizon it might seem that this information is lost. However this information is stored in the surface of the event horizon - thus the entropy of the black hole is related to the surface area of the black hole.

 

If you really want to crunch the numbers there are 3.838e69 planck areas per metre; and the entropy is proportional to a quarter of the surface area of the event horizon. The logarithm of the number of microstates (which is the entropy) of the material which took information into the black must therefore also be proportional to the surface area of the event horizon - this would be very closely related to the mass of the material which went in

 

 

 

[\tongue in check & devil's advocate]

[Robittybob1]

 

And how is dividing mass by area going to help?

it is like "pressure" e.g. pounds per square inch. If the EH is just a surface then the OP is a valid question "What difference does it make if the Schwarzschild radii Event Horizons touch?

It would be a totally different situation if there was extreme amounts of mass at that surface.

 

I need a bit of time to review the thread to see if I have misunderstood what has been said please.

Edited April 1, 2016 by Robittybob1

[Mordred]

Energy/density has the same units as pressure. The SI unit is joules/m^3.

 

https://en.m.wikipedia.org/wiki/Energy_density

Trying to define how thick the event horizon is ? Is rather pointless. Once you cross the outer surface for lack of better terminology the information is lost to us. We simply cannot retrieve any details past the surface.

 

Of course we also avoided talking about the amount of redshift involved.

 

As much as the Schwartzchild metric has its inherent problems it's probably the best starting point to understanding the event horizon.

 

I would suggest trying to understand that metric.

Edited April 1, 2016 by Mordred

[Robittybob1]

Energy/density has the same units as pressure. The SI unit is joules/m^3.

 

https://en.m.wikipedia.org/wiki/Energy_density

Trying to define how thick the event horizon is ? Is rather pointless. Once you cross the outer surface for lack of better terminology the information is lost to us. We simply cannot retrieve any details past the surface.

 

Of course we also avoided talking about the amount of redshift involved.

Does that mean we can't estimate the energy density of the EH but we could do it for the whole black hole?

[Mordred]

Essentially the mass of the blackhole defines the radius that the event horizon will occur.

 

Whether or not the interior of the BH is solid or singular (which we don't know) makes no difference to the Schwartzchild radius.

 

We can only estimate the total mass of the BH by its Schwartzchild radius.

Edited April 1, 2016 by Mordred

[Robittybob1]

I saw one paper that looked at the ringdown features to try and make some predictions about what was happening beyond the EH.

I can't say I understood their reasons.

Essentially the mass of the blackhole defines the radius that the event horizon will occur.

Whether or not the interior of the BH is solid or singular (which we don't know) makes no difference to the Schwartzchild radius.

But it will make a difference to the way the ringdown frequencies change.

[Mordred]

We would love to be able to gather datasets beyond the event horizon. It would have incredible applications towards quantum gravity etc.

The accretion paper I posted earlier this thread also suggests a possible method to garnish data of the interior of an event horizon. If I recall it was in section 6.

 

Again hypothetically.

 

But it will make a difference to the way the ringdown frequencies change.

I'm not sure about that without examining the paper

Edited April 1, 2016 by Mordred

[Robittybob1]

We would love to be able to gather datasets beyond the event horizon. It would have incredible applications towards quantum gravity etc.

I tried to review the thread but there seems to be more than one view. Do you agree with what Strange has been saying?

I can't read both of your posts (Mordred and Strange) and combine the ideas. I therefore can't review the thread. Unless each of you say yes I agree or disagree to a former post. Only then would I know you both are talking about the same concepts and they can be combined.

Edited April 1, 2016 by Robittybob1

[Mordred]

Is there a specific aspect your looking at that you perceive is different from my replies to Strange replies?

[Robittybob1]

Is there a specific aspect your looking at that you perceive is different from my replies to Strange replies?

look at posts #2 and #3 can both of those physical situations be married together.

[Mordred]

Are you referring to where the mass is in the interior of a BH? Ie the singularity or entirety of the interior.

 

We don't know. We can only hypothesize. We have no data of the interior conditions beyond the event horizon.

look at posts #2 and #3 can both of those physical situations be married together.

Ah ok. The answer given by Strange is more accurate. Yes the the energy/density increases as you approach the event horizon. Its in a sense controversial to say the mass density via the energy/mass equivalence increases. In some ways GR doesn't have a clear cut definition of mass.

 

For the purpose of what your trying to understand I would go with the reply by Strange

[Robittybob1]

Are you referring to where the mass is in the interior of a BH? Ie the singularity or entirety of the interior.

 

We don't know. We can only hypothesize. We have no data of the interior conditions beyond the event horizon.

http://arxiv.org/pdf/1506.00560.pdf "Possible golden events for ringdown gravitational waves" This was the paper making predictions about the internal structure of the BH.

 

If there is a lot of mass above the EH (#2) how can the two EHs instantly combine (#3). Do you agree the EH can change shape? (#3)

What happens if the EH is spinning as well? Can it change shape and spin at the same time. Where is that mass when it goes through these motions as well as orbiting each other.

Edited April 1, 2016 by Robittybob1