How Does a Black Hole's Gravity Vary Despite Its Infinite Density?

[danihel]

hi
first I am not a physicist/mathematician, i was said that black hole is this infinitely small point of infinite density and the amount of matter that collapsed into this point determines the diameter of event horizon and the overall gravitational pull of the black hole. My question is: how can the gravity of BH vary if its caused by this one infinitely small point of infinite density? are there larger or smaller infinities or what's the catch?

 

[Dmitry67]

the size of event horizon is determined by the mass.
your question is very good. How can one point be heavier than another?

1. elementary particles are also points, but they have different masses
2. nobody believes that singularity is actually a zero-volume point. Future theory must tell us that, for example, there is something different instead (without infinities)

 

[mathman]

The concept of a point with infinite density is the result of using general relativity without considering quantum theory. Inside a black hole these theories are incompatible - trying to use both at the same time leads to nonsensical solutions.

 

[Borek]

i was said that black hole is this infinitely small point of infinite density and the amount of matter that collapsed into this point determines the diameter of event horizon

We have no idea what BH is - we can only "see" its event horizon and the event horizon radius depends on the mass of what is inside. So from our point of view BH is the object of the radius of its event horizon. What happens inside stays inside.

 

[skeptic2]

We have no idea what BH is - we can only "see" its event horizon and the event horizon radius depends on the mass of what is inside. So from our point of view BH is the object of the radius of its event horizon. What happens inside stays inside.

Are we saying that the strength of gravity of a BH and the radius of the EV are due to the mass of the singularity inside the event horizon? Aren't we also saying that the singularity is the future for everything inside the event horizon so any increase in the force of gravity or curvature of spacetime must travel backwards in time to reach the EV?

 

[captn]

... BH and the radius of the EV are due to the mass of the singularity inside the event horizon?

We don't know if there is a singularity inside the event horizon---continuing the math inside the event horizon suggests a singularity, but perhaps not all possible factors have been taken into account. (Quantum effects, as suggested above, for instance.)


Neil

 

[Chronos]

The gravity of a black hole is identical in strength to that of the mass from which it formed. Black holes arise when mass condenses down to the point an event horizon forms. What happens beyond that is a guess. My guess is collapse halts at the Planck density - a miniscule, but, finite volume.

 

[stevebd1]

I always think that this gives a good explanation of what's going on with gravity around a black hole-

http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/black_gravity.html"

 

[skeptic2]

Thank you Stevebd1, unfortunately your reference leaves a number of unanswered questions. It begins by saying that gravity doesn’t have to get out of the black hole, that the gravitational field is defined by the star’s mass before its collapsed into a black hole and that the gravitational field is a “fossil field”. Presumably the gravitational field or warped spacetime is frozen due to time dilation at the event horizon. How is it then that matter is able to pass through the EH but its gravitational and electric fields do not?

Next it states that gravitons don’t exist in GR but goes on to use virtual photons as an analogy for how gravitons would behave if they did exist. In his analogy, McIrvin refers to a static electric field. Static electric and gravitational fields are not the issue. We are interested in how changes in the singularity’s mass are propagated to the event horizon. Other references, including Leonard Susskind if I’m not mistaken, talk about the gravitational field of an infalling object adding to the frozen gravitational field at the event horizon of the black hole. This explanation avoids the problem with the effects of changes in the mass of the singularity propagating backwards to the EH but still leaves us with the problem of matter being able to pass through the EH but its gravitational field remaining frozen at the event horizon. Isn’t a much simpler explanation that the electric and gravitational fields remain at the event horizon because infalling matter also remains at the horizon?

 

[Dmitry67]

Isn’t a much simpler explanation that the electric and gravitational fields remain at the event horizon because infalling matter also remains at the horizon?

No, because in case of collapsing star most of the matter (and charge if any) can be INSIDE the event horizon - from the very beginning. For example, the center of the collapsing star.

 

[skeptic2]

No, because in case of collapsing star most of the matter (and charge if any) can be INSIDE the event horizon - from the very beginning. For example, the center of the collapsing star.

No, I don't think that's an adequate explanation either. The matter near the center of a star before it implodes will be attracted toward the center of the star. This means that the event horizon must begin to form near the center of the star and expand rapidly outward as the star collapses. Each particle sees its own event horizon in the direction of the center.

 

[Dmitry67]

Are you aware that the position of the apparent event horzon is observer-dependent, so different particles don't argree where the star is 'frozen'?

 

[skeptic2]

Yes, that's what I intended to say.

 

[jnorman]

hey now - inre: "nobody believes that singularity is actually a zero-volume point"

i believe it. i try to believe at least 3 impossible things before breakfast each day - otherwise, you have to just give up on physics entirely :-)

 

[Patrus89]

No, I don't think that's an adequate explanation either. The matter near the center of a star before it implodes will be attracted toward the center of the star. This means that the event horizon must begin to form near the center of the star and expand rapidly outward as the star collapses. Each particle sees its own event horizon in the direction of the center.

What of a super-massive BH, where the event horizon forms well outside of a violent region? Take Hawking's oft used example of an astronaut who does not realize that he has passed the point of no return, continuing until tidal forces shred him like cheap mozzarella. The event horizon doesn't have to sweep out from the stellar core, but rather is a region that emerges and can do so far away from the center of collapse.

The OP asked what gives a BH its gravity, and the answer is the same thing that gives anything the same property, energy-momentum.

 

[Passionflower]

the size of event horizon is determined by the mass.
your question is very good. How can one point be heavier than another?

1. elementary particles are also points, but they have different masses
2. nobody believes that singularity is actually a zero-volume point. Future theory must tell us that, for example, there is something different instead (without infinities)

Please give a reference for your statement that elementary particles are points. A singularity a zero volume point? What singularity are you talking about?

The concept of a point with infinite density is the result of using general relativity without considering quantum theory. Inside a black hole these theories are incompatible - trying to use both at the same time leads to nonsensical solutions.

Could you give an example where in GR we can have a point with zero density?

 

[Dmitry67]

Please give a reference for your statement that elementary particles are points.

http://en.wikipedia.org/wiki/Point_particle

In particle physics, "point particle" is synonymous with "elementary particle", which is defined as a particle without structure or, equivalently, as a particle which is not made up from component parts. According to the Standard Model of fundamental particles and forces, quarks, leptons and the (non-composite) vector bosons are point particles in this sense. There is no experimental evidence for any of the elementary particles having spatial extent, and so they are usually considered to be point particles in the more general sense too (at least to the limited extent that the concept of a "particle" is meaningful in quantum field theory.)

A singularity a zero volume point? What singularity are you talking about?

Timelike in non-rotating BH (if 'observed' from infinity). For a falling observer it is spacelike.

Could you give an example where in GR we can have a point with zero density?

[/quote]

? empty space.
Every point has 0 density

 

[Passionflower]

There is no experimental evidence for any of the elementary particles having spatial extent, and so they are usually considered to be point particles in the more general sense too (at least to the limited extent that the concept of a "particle" is meaningful in quantum field theory.)

If there is no evidence that elementary particles are zero dimensional points then it not very scientific to make such a claim as if it were true. Would you agree with that?

Timelike in non-rotating BH (if 'observed' from infinity). For a falling observer it is spacelike.

So do you claim that whether a singularity is timelike or spacelike depends on the chosen coordinate chart and/or observer? I think there are no timelike singularities in a Schwarzschild spacetime.

Every point has 0 density

Actually empty space is not really empty, but at any rate it was a typo, I meant infinite density.

 

[Dmitry67]

1. There is not evidence that elementary particles are not zero-dimensional. But QFT is based on the assumtion that particles are point like. So if you claim that they are not (and hence QFT is wrong) then the burden of proof is yours

2. I was not clear. Look at standard singularity of non-rotating BH. In Kruskal–Szekeres coordinates singularity is in the future (of the free falling observer) and is space-like, in Eddington–Finkelstein coordinates singularity is a vertical line and it is timelike (but for an observer at infinity)

3. BH solutions have singularities in GR. The question if it is a point depends on how you look at it (if it is 3D space or 4D space) - in 4D it is not a point but a line. And of course, Quantum gravity should explain why singularity does not actually form.

 

[Passionflower]

2. I was not clear. Look at standard singularity of non-rotating BH. In Kruskal–Szekeres coordinates singularity is in the future (of the free falling observer) and is space-like, in Eddington–Finkelstein coordinates singularity is a vertical line and it is timelike (but for an observer at infinity)

This may be just a definition issue but why do you believe that the nature of a singularity depends on a chart and/or observer?

 

[Dmitry67]

You're right, singularity is objective so it should not depend on the choice of the coordinate system. Different coordinate systems have their 'time' oriented differently, so it gives different results.

For free falling observer, singularity is in fact not a point, it is in the future. But I guess it is more about semantics... I am thinking more in terms of Eddington–Finkelstein, so for me it is a point.

Also Kerr ring singularity is infinitely dense (in GR, without quantum gravity), and it is timelike in all senses!