Where to black holes end up?

[MigL]

4 hours ago, Markus Hanke said:

it’s much more accurate to say that there is an equivalence relationship between (Einstein, not Riemann!) curvature and energy-momentum.

Altering the configuration of a system will change its energy-momentum, resulting in a change in the local space-time 'curvature', and possible gravitational wave emission ?
Is that not a causal relation ?

[Ken Fabian]

@Markus Hanke Thanks for the reply. I have to admit my level of ignorance has not decreased by much; I will defer to people who know more than me and take it as given that the mass within black holes affecting space-time outside it with gravity isn't a contradiction.

[geordief]

24 minutes ago, Ken Fabian said:

@Markus Hanke Thanks for the reply. I have to admit my level of ignorance has not decreased by much; I will defer to people who know more than me and take it as given that the mass within black holes affecting space-time outside it with gravity isn't a contradiction.

I think the mass within black holes could not emit gravitational waves beyond the EH and so could not change the gravitational  field outside the EH is what I imagine might account for that.

Actually  I wonder what would happen to those gravitational waves.Do they build up in some kind of cosmic  traffic jam at the EH red traffic lights,? Do they self interfere?

 

I suppose  the BH might influence   the  gravitational  field in a negative way 

 

As stars are sucked into the BH their mass is lost  and so the outside gravitational  field  changes accordingly (unless the outside gravitational field never "sees" objects actually  falling into the EH? Is  that supposed to  happen?)

 

 

 

 

[MigL]

6 minutes ago, geordief said:

I think the mass within black holes could not emit gravitational waves beyond the EH and so could not change the gravitational  field outside the EH is what I imagine might account for that.
Actually  I wonder what would happen to those gravitational waves.Do they build up in some kind of cosmic  traffic jam at the EH red traffic lights,? Do they self interfere?

The classically conserved quantity we associate with 'mass' is essentially encoded in the event horizon.
As such it is a measure of the local space-time curvature.

For all we know ( classically ) there is nothing inside a BH.
Gravitational waves are only observable outside the event horizon, and any 'internal', if possible, would simply contribute to energy-momentum of the system, due to self interaction.

[Markus Hanke]

6 hours ago, MigL said:

Altering the configuration of a system will change its energy-momentum, resulting in a change in the local space-time 'curvature', and possible gravitational wave emission ?
Is that not a causal relation ?

If you restrict your attention to some small region away from the source, through some limited period of time, then you could speak of a causal relationship in a purely local sense - something changed at the source, and awhile later my originally flat patch contains waves.

Globally though, across all of spacetime, it’s still an equivalence - a time-dependent source distribution is equivalent to a time-dependent Einstein tensor. The global metric actually doesn’t change at all here, in the sense that its covariant derivative always vanishes.

This is pretty subtle stuff.

6 hours ago, Ken Fabian said:

take it as given that the mass within black holes affecting space-time outside it

You see, the issue here is that there is no mass “inside” that somehow affects spacetime “outside”. In fact, in ordinary Schwarzschild spacetime there is no mass anywhere - it’s a vacuum solution that’s everywhere empty. It’s thus meaningless to point at any single point or region and say that’s where the mass is. The black hole is actually the entire spacetime; so mass is a global property, not local.

[geordief]

1 hour ago, Markus Hanke said:

If you restrict your attention to some small region away from the source, through some limited period of time, then you could speak of a causal relationship in a purely local sense - something changed at the source, and awhile later my originally flat patch contains waves.

Globally though, across all of spacetime, it’s still an equivalence - a time-dependent source distribution is equivalent to a time-dependent Einstein tensor. The global metric actually doesn’t change at all here, in the sense that its covariant derivative always vanishes.

This is pretty subtle stuff.

You see, the issue here is that there is no mass “inside” that somehow affects spacetime “outside”. In fact, in ordinary Schwarzschild spacetime there is no mass anywhere - it’s a vacuum solution that’s everywhere empty. It’s thus meaningless to point at any single point or region and say that’s where the mass is. The black hole is actually the entire spacetime; so mass is a global property, not local.

Is it possible  to talk of a frame of reference beyond(ie within) the EH?

I assume it must in,ar least some  sense because  we talk about  the inability of objects,including  massless objects "escaping " the interior of   BH

 

1 hour ago, Markus Hanke said:

Globally though, across all of spacetime, it’s still an equivalence - a time-dependent source distribution is equivalent to a time-dependent Einstein tensor. The global metric actually doesn’t change at all here, in the sense that its covariant derivative always vanishes.

Demarcated causality? ( there is no  domino effect?)

6 hours ago, MigL said:

classically conserved quantity we associate with 'mass' is essentially encoded in the event horizon

And yet objects pass through the EH  in real time without noticing any changes?

They don't run into a cosmic brick wall.

 

[Moontanman]

I have to ask, what type of black holes is everyone discussing? How about a charged rotating black hole? Would these attributes change the conversation? If so in what ways?  

[MigL]

17 hours ago, geordief said:

And yet objects pass through the EH  in real time without noticing any changes?
They don't run into a cosmic brick wall.

A simple, non-rotating, non-charged Schwarzschild BH has the concept of mass encoded in the size of the EH; increase the mass ( by injesting material ) and the size ( radius ) of the EH increases.
The EH is a mathematical construct, not a massive object like a brick wall.

Rotating BHs ( Kerr ) and charged  BHs ( Reissner-Nordstrom ) ecode angular momentum and charge in differently configured ( multiple ) EHs.

[Markus Hanke]

22 hours ago, geordief said:

Is it possible  to talk of a frame of reference beyond(ie within) the EH?

Yes, sure. Local physics in the interior follow the same laws as anywhere else (singularity aside).

22 hours ago, geordief said:

Demarcated causality? ( there is no  domino effect?)

Not sure what you mean by this...

22 hours ago, geordief said:

And yet objects pass through the EH  in real time without noticing any changes?

The mass is encoded in the sense that the surface area of the EH is a function of said mass. But it doesn’t mean that the mass is concentrated into a shell of some kind. The EH is a region of empty and regular spacetime, so you can fall through it.

16 hours ago, Moontanman said:

 

I have to ask, what type of black holes is everyone discussing?

 

Schwarzschild black holes.

16 hours ago, Moontanman said:

How about a charged rotating black hole? Would these attributes change the conversation? If so in what ways?  

The same principles hold for all the Kerr-Schild metrics (which are electro-vacuum solutions), in that all parameters in the metric are global properties of the entire spacetime, and not localisable. This is thus true also for charge and angular momentum.

[geordief]

6 hours ago, Markus Hanke said:

Not sure what you mean by this

Not to worry.

I am sure if I was expressing  myself clearly (or if I had something in my mind or a question that was  worth expressing) you would have understood it.

 

Looking forward to the  new pictures from the JWT telescope  from tonight onwards 🙂

Edited July 12, 2022 by geordief

[Moontanman]

7 hours ago, Markus Hanke said:

Yes, sure. Local physics in the interior follow the same laws as anywhere else (singularity aside).

Not sure what you mean by this...

The mass is encoded in the sense that the surface area of the EH is a function of said mass. But it doesn’t mean that the mass is concentrated into a shell of some kind. The EH is a region of empty and regular spacetime, so you can fall through it.

Schwarzschild black holes.

The same principles hold for all the Kerr-Schild metrics (which are electro-vacuum solutions), in that all parameters in the metric are global properties of the entire spacetime, and not localisable. This is thus true also for charge and angular momentum.

Would charge and or rotation change the size of the volume of the event horizon? Would a ring singularity form in a rotating black hole? Could charge expand the radius of the event horizon by electric charge repulsion? Since the electromagnetic force is stronger than gravity could sufficient charge cause a black hole to expand until it had no event horizon? 

[Halc]

1 hour ago, Moontanman said:

Would charge and or rotation change the size of the volume of the event horizon? Would a ring singularity form in a rotating black hole? Could charge expand the radius of the event horizon by electric charge repulsion? Since the electromagnetic force is stronger than gravity could sufficient charge cause a black hole to expand until it had no event horizon? 

The event horizon is a null surface, and as such has a coordinate area, not volume. I'm not sure of the relationship between this area and its angular momentum, all else being equal.

Yes, a rotating black hole (Kerr metric) contains a ring singularity.

A charged black hole (Reissner-Nordsrom metric) cannot have its charge exceed its mass. So no additional charge can be added to one that is sufficiently close. The mass in unaffected by this, and the event horizon 'radius' is determined by the mass.

If there is a black hole with charge equal to its mass, you get a naked singularity, which is a singular solution to the metric. So (just thinking out loud here, not an authority), if you have a super-positive charged black hole near this limit, a negatively charged particle would be more attracted to it than a neutral particle. Thus I would think there would be a second charged event horizon for the negatively charged thing that is further out than that of say a neutrino. Also, the EM potential would be so steep that it would probably rip apart (an EM 'tidal' effect) neutral things like a neutron, pulling it into charged components and accepting only the one.

[MigL]

A Kerr ( rotating ) BH also has two event horizons.

See here         Rotating black hole - Wikipedia

As with Reissner-Nordstrum ( charged ) or Kerr-Newman ( rotating and charged ), certain values of spin ( angular momentum ), if exceeded, will cause the inner horizon to move outside the outer horizon, leaving a 'naked' singularity. That is what I have read; my math is not advanced enough to 'interpret' the Kerr metric that way.
Naked singularities are even more absurd and non-sensical than plain singularities, which must always be hidden by an event horizon.

For the reasons presented by Halc above, charged BHs would be extremely rare, if possible, as they tend to 'neutralize' themselves, and a Schwarzschild ( non-rotating ) BH is almost impossible, as collapse increases even the smallest amount of spin ( 'ice skater drawing in her arms'  effect ).
The most viable solution for almost all BHs, is the Kerr metric or a rotating BH.

[Markus Hanke]

8 hours ago, Moontanman said:

Would charge and or rotation change the size of the volume of the event horizon?

The event horizon surface area is a function of mass, charge, and angular momentum. The 3-volume enclosed by this surface depends on the observer, so that can’t be answered in general (the actual calculation itself would also be quite cumbersome). Bear in mind also that the EH is now no longer a sphere, so talking about “radius” will depend on the latitude.