Can Gravity Escape a Black Hole?

[Vandenburg]

TL;DR

If light can't escape a black hole, how can gravity?

If:

1. Gravity propagates via "particles" of gravity, and
2. The particles of gravity are massless and so move at the speed of light

then how can the gravity particles escape from a black hole? Aren't they as trapped as the photons? It seems as if black holes should present no gravitational field at all.

(Ok, I just found Can gravity escape a black hole? I *did* search for an answer before I posted!)
(But I don't understand the explanation.)

 

[Nugatory]

If:

1. Gravity propagates via "particles" of gravity, and

….

It doesn’t.

All the gravitational effects of a black hole are caused by spacetime curvature outside the event horizon.

 

[Vandenburg]

It doesn’t.

All the gravitational effects of a black hole are caused by spacetime curvature outside the event horizon.

Yes, I saw that in one of the other threads. But I don't understand it. How does the spacetime curvature maintain itself once the gravity that caused it becomes unavailable? If I moved the black hole somewhere else, would the curved spacetime just remain where it was, causeless?

 

[Dale]

If I moved the black hole somewhere else, would the curved spacetime just remain where it was, causeless?

Assuming the black hole was formed by some sort of collapse, then the collapsing matter is and remains the cause. Well, that and whatever stress energy you use to move it.

 

[Vandenburg]

Again, if the collapsing matter remains the cause of the spatial curvature, how can the matter inside the event horizon have that (or any other) effect outside that horizon? How can gravitons from inside escape? Or must I believe that gravity is not quantized?

 

[Dale]

if the collapsing matter remains the cause of the spatial curvature, how can the matter inside the event horizon affect events outside that horizon?

It doesn’t. It is the collapsing matter outside the horizon during the collapse that affects events outside the horizon.

You appear to be forgetting that causes happen in the past. The fact that the matter is now in the horizon is not particularly relevant for causality. What is important is what happens in an event’s past light cone. The horizon is never in the past light cone of any event outside. The collapsing matter is.

 

[Vandenburg]

Let me think about that a bit.
All right, I have to confess I have always thought of a black hole as looking something like a bowling ball. Thinking about it, I realize that the black hole would normally form, leaving a great deal of matter still outside it. My bowling ball becomes a storm cloud.
But given that a black hole does sit at the center of a deeply curved bit of space, eventually would it not pull all of the nearby matter into the event horizon? Would it not eventually become like my bowling ball? Would it then cease to dent spacetime?

 

[PeterDonis]

I have to confess I have always thought of a black hole as looking something like a bowling ball.

This is not a correct picture. See below.

Would it then cease to dent spacetime?

The "dent" picture is not a picture of spacetime, it's a picture of space; a gravitating mass is pictured as making a "dent" in space, which is deeper the denser the mass is.

However, this picture cannot be applied to a black hole, because it does not work with an object that has an event horizon. It only works for objects like planets and stars that do not have an event horizon.

 

[Vandenburg]

Ok, so how does that apply? Will a black hole which is not surrounded by a cloud of matter -- one which has pulled all the available matter into its event horizon -- will such an object present as a source of gravity?

 

[PeterDonis]

so how does that apply?

How does what apply?

Will a black hole which is not surrounded by a cloud of matter -- one which has pulled all the available matter into its event horizon -- will such an object present as a source of gravity?

Yes. And from far away, it will look the same as any other source of gravity with the same mass; you can still use the "dented space" picture far away from the hole, just as you would for a star of the same mass as the hole. But you can't use it close to the hole or inside the hole's horizon, which means you can't use it to form a complete understanding of what the hole is or how it works, including how the spacetime geometry around the hole is maintained.

 

[Dale]

Will a black hole which is not surrounded by a cloud of matter -- one which has pulled all the available matter into its event horizon -- will such an object present as a source of gravity?

That is what I already described. Remember, causes are in the past, specifically inside the past light cone. At any event outside the horizon the past light cone does not include the horizon, but it does include the collapsing matter. That includes events where the present black hole is fully collapsed with no remaining matter.

 

[PeterDonis]

events where the present black hole is fully collapsed with no remaining matter.

Can you give a specific example of such an event?

 

[Dale]

Can you give a specific example of such an event?

Sure, here is a Kruskal diagram of a collapsing black hole:

The dark red event is such an event. If you go to the left you see that the matter has all collapsed at the present time (in Kruskal coordinates), but if you follow the yellow past light cone back you see that it intersects the white line which is the collapsing star prior to the formation of the horizon.

 

[DaveC426913]

But given that a black hole does sit at the center of a deeply curved bit of space, eventually would it not pull all of the nearby matter into the event horizon?

No more or less than any other object of the same mass.

If you were in a spaceship orbiting an object of, say, 10 solar masses, you would follow the same path, whether the object were a 10 solar mass star or a 10 solar mass black hole (providing your orbit isn't so close as to intersect the object). And if your spaceship had no windows, you couldn't (easily) tell which one you were orbiting. Neither could any gas or dust in an accretion disk

 

[PeterDonis]

The dark red event is such an event. If you go to the left you see that the matter has all collapsed at the present time (in Kruskal coordinates), but if you follow the yellow past light cone back you see that it intersects the white line which is the collapsing star prior to the formation of the horizon.

So basically it's an event that is outside the horizon in the vacuum region, but close enough to the horizon that it has the collapsing matter in its past light cone?

 

[Dale]

So basically it's an event that is outside the horizon in the vacuum region, but close enough to the horizon that it has the collapsing matter in its past light cone?

Yes. And note that I am using Kruskal simultaneity and not Schwarzschild. I don’t know if such events exist in Schwarzschild coordinates. The light cones are more difficult to trace.

 

[PeterDonis]

note that I am using Kruskal simultaneity and not Schwarzschild.

Yes, to define a "time that the collapse crossed the horizon" (or anything similar that can serve as a "time the black hole formed", you have to use a simultaneity convention other than Schwarzschild. Painleve or Eddington-Finkelstein would also work.

 

[PeterDonis]

I don’t know if such events exist in Schwarzschild coordinates.

You can give an invariant definition for such an event: basically it needs to be in the vacuum region, and at an $r$ coordinate greater than $2M$ but close enough to it that that $r$ coordinate (or more precisely the areal radius corresponding to it) will have been traversed by the collapsing matter. (Basically this would be any areal radius smaller than the original areal radius of the star before it collapsed.)

Such a region can in fact be defined in terms of Schwarzschild coordinates, but it will not look nearly as simple, both because, as you note, the light cones look a lot more complicated, and because the surface of the collapsing matter looks a lot more complicated (since it never actually reaches $2M$ anywhere in the Schwarzschild exterior coordinate patch).

 

[ersmith]

I think the original question is due to a confusion between virtual and real particles. In a hypothetical theory of quantum gravity, real gravitons would be the particles that make up gravitational waves, and they certainly could not escape a black hole (just as real photons making up light waves cannot). However, gravitational attraction would be modeled by exchange of *virtual* gravitons. There are some good insights articles elsewhere on this site describing the difference between virtual and real particles. The bottom line is that one should not think of virtual particles as real; they are more like book keeping devices than actual "things" moving through spacetime.

Similarly, a charged black hole can attract or repel appropriately charged particles. This can be modeled as virtual photons interacting with the charged particles, but there's no contradiction with the fact that real photons cannot escape a black hole. What's "really" happening is that both the black hole and the outside (real) particles are interacting with the electromagnetic field, just as in the gravitational case both are interacting with the "gravitational field" (spacetime).

 

[vanhees71]

I'd not use "quantum lingo" in this context. Classical field theory is all you need, and it's clear that outside the event horizon a black hole just has a gravitational field (aka spacetime curvature) around it as any other body of this mass. As the most simple example take the Schwarzschild black hole as an example. If it has also electric charge (the Reisner-Nordström solution) there's also the usual electrostatic Coulomb field around it.

 

[anuttarasammyak]

It doesn’t. It is the collapsing matter outside the horizon during the collapse that affects events outside the horizon.

You appear to be forgetting that causes happen in the past. The fact that the matter is now in the horizon is not particularly relevant for causality. What is important is what happens in an event’s past light cone. The horizon is never in the past light cone of any event outside. The collapsing matter is.

Some years ago I made a practice of integrating energy-stress pseudo tensor density in all the space outside the Schwartzshild horizon of BH and got the same value as mass of BH. Does it suggest that all the energy of Schwartzshild BH lies outside the horizon and coincide with the view you explained ?

May we say that all the BHs gravity of which originates from once falling or collapsing ordinary matters are born after big bang or beginning of the Universe ? Because if there were no generation process or making history of BHs, we could not observe gravity from these BHs following your explanation.

Thanks.

 

[Dale]

Because if there were no generation process or making history of BHs, we could not observe gravity from these BHs following your explanation.

Don’t forget that in an “eternal” Schwarzschild spacetime there is also a white hole. The singularity of the white hole is in the past light cone of every event in the spacetime. That would be the cause of gravity in that spacetime.

To me, that is one reason to assume that black holes will come from collapse, and “eternal” black holes are likely to be fictional