What difference does it make if the Schwarzschild radii touch?

[swansont]

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 ...)

In the BH's frame, sure. But one could read this as saying that there will be no length contraction if one has a large relative speed with respect to the BH. That doesn't seem right.

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.

The definition you quoted says explicitly that it's a sphere. So I don't know where this objection is coming from.

[Mordred]

Gravity doesn't get out of the event horizon.

 

The gravitational mass information is stored at the event horizon.

 

Kind of a difficult concept to grasp

 

Without the math here is a simple explanation.

http://physics.stackexchange.com/questions/937/how-does-gravity-escape-a-black-hole

 

Essentially the gravitational field resides at the event horizon.

[Robittybob1]

 

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

 

 

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

 

 

Why would the speed change its shape?

If the mass was not situated at the singularity, that is fine by me but how do you get that mass to orbit at different speeds and stay together as a BH? You must be dealing with new physics if that can happen.

If the center of a BH about to contact another BH is going at 0.5c how fast is the mass going on the non-contacting side? Can you have mass at that distance at that speed and maintain an orbit?

[Carrock]

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

To save me reading through your entire reference, please quote the claim that accretion discs must exist whether or not matter is falling towards the black hole.

 

 

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.

You seem to be claiming that black holes create positive gravitational energy and some of this creates gravity waves during mergers.

You're ignoring my post #15, particularly the last line.

 

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

AFAIK no one is missing that fact.

[Mordred]

I didn't claim all blackholes have accretion disks Carrock. However any positive energy/density region still has mass.

 

You don't have to read the entire reference just look at equation 43.

 

Or section 3 of that reference.

 

 

Why do you think the stress energy tensor includes [latex]\rho[/latex]

 

Which is energy or mass density.

 

https://en.m.wikipedia.org/wiki/Stress%E2%80%93energy_tensor

Edited March 31, 2016 by Mordred

[Robittybob1]

In the BH's frame, sure. But one could read this as saying that there will be no length contraction if one has a large relative speed with respect to the BH. That doesn't seem right.

 

The definition you quoted says explicitly that it's a sphere. So I don't know where this objection is coming from.

if the definition says it is a sphere I'm never going to use the word Schwarzschild radius ever again in relation to orbiting BHs, we'll just have to call it something else that allows it to change shape. "Event horizon" maybe

Wikipedia event horizon:

 

The surface at the Schwarzschild radius acts as an event horizon in a non-rotating body that fits inside this radius (although a rotating black hole operates slightly differently).

Edited March 31, 2016 by Robittybob1

[Carrock]

I didn't claim all blackholes have accretion disks Carrock. However any positive energy/density region still has mass.

We're entirely agreed; the latter sentence is not contentious.

 

You don't have to read the entire reference just look at equation 43.

 

Or section 3 of that reference.

From the reference

equation 43 is a mathematical formulation of energy and mass conservation laws; there is no suggestion black holes create energy or a nearby 'positive energy/density region' which would violate conservation laws.

 

As I've mentioned before, there is a convention on this site that it should be possible to follow posts without going offsite.

I'm certainly not going to read section 3 to try and guess its relevance.

[Strange]

Wikipedia:

Where does the mass of a BH reside?

 

Inside the black hole. Or possibly at the event horizon. You can't tell the difference (see Newton's shell theorem and the no hair theorem).

 

Did Schwarzschild ever envision a BH moving at half the speed of light?

 

Relative to what?

 

But no. The Schwarzschild solution only applies to a static, non-rotating, uncharged black hole in an empty universe. It is a useful approximation in other, slightly more realistic cases, as well.

 

A rotating black hole is described by the Kerr metric.

Gravity gets out through the event horizon agreed?

 

No it doesn't.

 

Do gravitons have mass?

 

No. They travel at the speed of light remember.

 

Does gravitational waves have energy hence a type of mass equivalence?

 

Yes. So does a static gravitational field. Which is why gravity is so non-linear.

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

 

No, as in: non-spherical.

In the BH's frame, sure. But one could read this as saying that there will be no length contraction if one has a large relative speed with respect to the BH. That doesn't seem right.

 

It doesn't seem right, I agree. But I am fairly sure that is what I have read... Would love to have it confirmed or corrected.

If the mass was not situated at the singularity, that is fine by me but how do you get that mass to orbit at different speeds and stay together as a BH?

 

What do you mean "stay together as a BH"? A black hole is indivisible. It isn't made of matter (probably). The singularity is mathematical result that is probably wrong. IGNORE IT. It is is irrelevant.

[swansont]

if the definition says it is a sphere I'm never going to use the word Schwarzschild radius ever again in relation to orbiting BHs, we'll just have to call it something else that allows it to change shape.

There's no "if" here. You quoted the definition; you're perfectly capable of going back a page and looking at it and going back to the wikipedia page (where it in fact tells you that the surface is the same as the event horizon). But — and this is a very important concept in physics — if you go through the derivation, you will see that the assumptions were "a non-rotating, spherically symmetric body" You HAVE to know the assumptions that come with an equation, otherwise you will end up applying it in conditions where it is invalid.

 

While the concept of having a surface inside of which nothing can escape still applies, the Schwarzschild radius equation does not apply to a binary system of any sort. It applies only to a single, nonrotating, spherically symmetric body.

[Strange]

 

If the center of a BH about to contact another BH is going at 0.5c how fast is the mass going on the non-contacting side? Can you have mass at that distance at that speed and maintain an orbit?

 

You can only know about the event horizons.

You can only know about the event horizons.

You can only know about the event horizons.

You can only know about the event horizons.

You can only know about the event horizons.

[Robittybob1]

Gravity doesn't get out of the event horizon.

 

The gravitational mass information is stored at the event horizon.

 

Kind of a difficult concept to grasp

 

Without the math here is a simple explanation.

http://physics.stackexchange.com/questions/937/how-does-gravity-escape-a-black-hole

 

Essentially the gravitational field resides at the event horizon.

That is just a whole lot more questions and answers.

[Mordred]

We're entirely agreed; the latter sentence is not contentious.

 

 

If we're agreed on this part we don't need the reference

[swansont]

It doesn't seem right, I agree. But I am fairly sure that is what I have read... Would love to have it confirmed or corrected.

 

I've never run across it.

 

I know it comes up in the context of an arbitrary star and its apparent density seen by a relativistic observer, and the notion that it might become a black hole (which it can't), but AFAIK that's because the conditions would not be invariant rather than the Schwarzschild radius being invariant. The calculation is only meaningful in the black hole's rest frame.

[Robittybob1]

 

Inside the black hole. Or possibly at the event horizon. You can't tell the difference (see Newton's shell theorem and the no hair theorem).

 

 

Relative to what?.....

 

What do you mean "stay together as a BH"? A black hole is indivisible. It isn't made of matter (probably). The singularity is mathematical result that is probably wrong. IGNORE IT. It is is irrelevant.

If the mass is inside the BH or even at the EH how does gravity get out? Light can't but gravity can, there seems to be a difference. OK I might be behind the times but are you saying we should never use the word "singularity" ever when describing a BH?

 

Seems to be used extensively in Wikipedia still

 

 

Singularity

Main article: Gravitational singularity

At the center of a black hole, as described by general relativity, lies a gravitational singularity, a region where the spacetime curvature becomes infinite.[59] For a non-rotating black hole, this region takes the shape of a single point and for a rotating black hole, it is smeared out to form a ring singularity that lies in the plane of rotation.[60] In both cases, the singular region has zero volume. It can also be shown that the singular region contains all the mass of the black hole solution.[61] The singular region can thus be thought of as having infinite density.

.

 

You can only know about the event horizons.

You can only know about the event horizons.

You can only know about the event horizons.

You can only know about the event horizons.

You can only know about the event horizons.

All those equations for the amplitude of the gravitational wave were based on the the CoM of the BH not the event horizon http://www.scienceforums.net/topic/94060-what-is-the-best-3d-description-of-gravitational-waves/page-3#entry913453. You guys have got me lost. You seem to know something I don't. How can we do calculations from the center of a BH if we can't know about it?

[Mordred]

Gravity doesn't get out the event horizon. The information of the mass of the singularity is in the gravitational field at the event horizon. Not in,

Edited March 31, 2016 by Mordred

[Robittybob1]

Gravity doesn't get out the event horizon. The information of the mass of the singularity is in the gravitational field at the event horizon. Not in,

Does the event horizon have no thickness? Is it a surface with no or only very small depth. Has it got a depth dimension? Is it a physical object and not just a distance? Wikipedia on Event horizon:

 

In general relativity, an event horizon is a boundary in spacetime beyond which events cannot affect an outside observer. In layman's terms, it is defined as "the point of no return", i.e., the point at which the gravitational pull becomes so great as to make escape impossible. An event horizon is most commonly associated with black holes.

.They make the event horizon sound more like a distance rather than a physical object.

Edited March 31, 2016 by Robittybob1

[Carrock]

We're entirely agreed; the latter sentence is not contentious.

 

 

If we're agreed on this part we don't need the reference [to mass-energy conservation laws].

 

You don't need the reference to claim that black holes create positive gravitational energy i.e. 'a region of higher gravitational potential' in violation of those conservation laws.

 

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

 

As you will not clearly state whether you consider gravitational energy to be positive, at least where black holes are concerned, in violation of conservation laws, I'm done here.

[Mordred]

Even the cosmological constant has positive energy density Carrock.

 

 

A void region in space away from all sources of gravitational energy has an average energy density of 7.52 *10 ^-10 joules/ m^3.

 

You can calculate that value via the critical density formula

 

Which correlates to roughly 5 protons per m^3. The average energy density of the interstellar medium within galaxies being a higher energy density. On average 15 times higher.

 

As you approach a massive object the average energy/density increases via the stress/energy tensor

Edited March 31, 2016 by Mordred

[swansont]

All those equations for the amplitude of the gravitational wave were based on the the CoM of the BH not the event horizon http://www.scienceforums.net/topic/94060-what-is-the-best-3d-description-of-gravitational-waves/page-3#entry913453. You guys have got me lost. You seem to know something I don't. How can we do calculations from the center of a BH if we can't know about it?

 

Because everyone else in the discussion is probably familiar with Gauss's law, which you learn in introductory physics. If you have a spherically symmetric mass distribution, it behaves as if all the mass was at the center. Put another way, knowing the gravitational force doesn't tell you anything about where the mass is actually located, only where its center is located. So R in all of these equations is to the center of the mass distribution.

https://en.wikipedia.org/wiki/Gauss's_law_for_gravity

 

Knowing the basics makes learning the advanced stuff so much easier. (arguably, makes it possible. You are going to miss a lot by not knowing the basics. It's blatantly obvious that this has already happened — often — in your many discussions)

[Mordred]

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

Edited March 31, 2016 by Mordred

[imatfaal]

Mordred - surely in terms of the s'child radius you must be able to consider the black hole without considering ANY content outside - the schwartzchild radius is the product of the vacuum solution to the field equations for a non-rotating non-charged black hole; with my emphasis being on a vacuum solution. You also get a solution to the field equations which gives a hawking-penrose spacelike singularity at the centre of a black hole. I realise that this work causes more problems that it answers in that no one really believes this is a correct model of reality - but it is GR and the best we have at present; it might have shown where we need an alternative to GR but I didn't think we had one yet

 

I do not see how these two sets of solutions are compatible with your assertions that you cannot look at black holes in isolation and that mass / gravity is a shell at the EH

[Robittybob1]

 

Because everyone else in the discussion is probably familiar with Gauss's law, which you learn in introductory physics. If you have a spherically symmetric mass distribution, it behaves as if all the mass was at the center. Put another way, knowing the gravitational force doesn't tell you anything about where the mass is actually located, only where its center is located. So R in all of these equations is to the center of the mass distribution.

https://en.wikipedia.org/wiki/Gauss's_law_for_gravity

 

Knowing the basics makes learning the advanced stuff so much easier. (arguably, makes it possible. You are going to miss a lot by not knowing the basics. It's blatantly obvious that this has already happened — often — in your many discussions)

Worth thinking about. CoM rather than actual mass.

[Mordred]

Mordred - surely in terms of the s'child radius you must be able to consider the black hole without considering ANY content outside - the schwartzchild radius is the product of the vacuum solution to the field equations for a non-rotating non-charged black hole; with my emphasis being on a vacuum solution. You also get a solution to the field equations which gives a hawking-penrose spacelike singularity at the centre of a black hole. I realise that this work causes more problems that it answers in that no one really believes this is a correct model of reality - but it is GR and the best we have at present; it might have shown where we need an alternative to GR but I didn't think we had one yet

 

I do not see how these two sets of solutions are compatible with your assertions that you cannot look at black holes in isolation and that mass / gravity is a shell at the EH

Yeah I've had this argument before on physicsforum.

 

The problem I've always had with the Schwartzchild child metric is the assumption of Euclidean flat being of zero energy density.

 

At no point in the universe is there a zero energy/density.

 

There is always the presence of some non zero field, for example the Higgs field itself.

The term vacuum doesn't mean zero energy/density.

Thankfully we can set the background metric as zero even if the background metric is a positive energy/density.

Edited March 31, 2016 by Mordred

[Robittybob1]

....

I do not see how these two sets of solutions are compatible with your assertions that you cannot look at black holes in isolation and that mass / gravity is a shell at the EH

Who was the scientist who first proposed this type of BH?

[Strange]

All those equations for the amplitude of the gravitational wave were based on the the CoM of the BH not the event horizon http://www.scienceforums.net/topic/94060-what-is-the-best-3d-description-of-gravitational-waves/page-3#entry913453. You guys have got me lost. You seem to know something I don't. How can we do calculations from the center of a BH if we can't know about it?

 

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.

Does the event horizon have no thickness? Is it a surface with no or only very small depth. Has it got a depth dimension? Is it a physical object and not just a distance?

 

It is a distance from the centre.