Slight confusion with black holes

[zewpals]

Hey, I am a little confused with the nature of black holes.

I am under the impression that time is infinitely slow at a black hole's existence.
I am also under the impression that black holes are a point of singularity, but have a defined mass.

Gravitational force is only caused by mass, right? How could time be infinitely slow if a mass is not infinitely large? Which of my statements is misguided?

 

[FawkesCa]

the mass of a black hole AT THE SINGULARITY is infinite. that doesn't make any sense to physicists today, that's why they are looking into other theories to help explain this discrepency in the math.

 

[zewpals]

Hmm, alright...It seems to deny energy/mass balances though if a large star were to suddenly become a point of singularity and have more mass than before. Where the heck does this other mass come from?

 

[FawkesCa]

Hmm, alright...It seems to deny energy/mass balances though if a large star were to suddenly become a point of singularity and have more mass than before. Where the heck does this other mass come from?

ummm... yeah... why do you think there is a rift in ALL OF PHYSICS. this is the question that is that Dr. Kaku and others are going nuts over. while doing the math of black holes, each and every time the mass of the black hole comes out to be infinite. strange, i know, both why do you think Einstein just ignored this problem... it was too crazy to even think of back then. but now that we know black holes exist, something has to change. its either GR is wrong or QM is wrong. but both work perfectly until we reach this problem. if you can figure it out, then buy a ticket to Norway... your Nobel Prize is waiting

 

[Chalnoth]

Hmm, alright...It seems to deny energy/mass balances though if a large star were to suddenly become a point of singularity and have more mass than before. Where the heck does this other mass come from?

This isn't correct. It doesn't have more mass than before. In a black hole in classical General Relativity, all of the mass is simply concentrated at the center of the black hole. It doesn't have infinite mass at all, just infinite density.

Now, we don't expect that a real black hole is actually this way. We expect quantum gravity will sort of smooth-out the singularity so that it has a large but still finite density. But we just don't yet know what the correct theory of quantum gravity is, so we can't say for certain what goes on inside a black hole.

 

[FawkesCa]

yea, sry, meant density, not mass. my bad

 

[Chronos]

Personally, I'm partial to the Planck density as the ultimate density limit. It avoids the problems that typically plague anything labeled as 'infinite' in our universe.

 

[George Jones]

For a classical black hole, the local mass density is zero every, because the stress-energy tensor in zero everywhere. As Chalnoth said, quantum gravity could change this.

 

[Chalnoth]

For a classical black hole, the local mass density is zero every, because the stress-energy tensor in zero everywhere. As Chalnoth said, quantum gravity could change this.

...everywhere but the singularity, you mean.

 

[George Jones]

...everywhere but the singularity, you mean.

I mean everywhere. The singularity is not part of the spacetime manifold. In fact, it is very difficult to give a definition of "singularity" . I think that there no accepted general definition, and that there is still ongoing mathematical research with respect to this. These attempts try to define singularities as boundary points to spacetime that are not actually in spacetime. It is easier to give a definition of "singular spacetime manifold", but, again, singular spacetimes don't have singularities as part of the spacetime manifold.

 

[Passionflower]

I am under the impression that time is infinitely slow at a black hole's existence.

A local clock always goes at one second per second. It is only when you compare two clocks that their time could be out of sync. A free falling observer under the gravitational attraction of a black hole will not notice anything with his clock. He will travel inertially (although there are non-local tidal accelerations), without any effect pass the event horizon and eventually, and unannounced, seize to exist at the singularity.

Gravitational force is only caused by mass, right? How could time be infinitely slow if a mass is not infinitely large? Which of my statements is misguided?

Gravitation is caused by potentially any component of the stress-energy tensor, which include energy, momentum, stress and pressure. The mass is not infinitly large but the gravitational force can be infinite in some cases, for instance at the black holes event horizon the perceived gravitational force is infinite for some observers.

 

[FawkesCa]

i have always hated the idea of a singularity. seems to me that if gravity is described as a bending of the "fabric" of space-time then that fabric has to have some sort of surface tension. i know is sounds stupid, and a lot of people have laughed and called me stupid over it, but it just makes sense in my mind. that's why I am going back to school at age 30 to get the knowlage to back me up. just seems logical that if something is dense enough, the foam of the universe eventually rips.

but that's just me

 

[Chalnoth]

A local clock always goes at one second per second. It is only when you compare two clocks that their time could be out of sync. A free falling observer under the gravitational attraction of a black hole will not notice anything with his clock. He will travel inertially (although there are non-local tidal accelerations), without any effect pass the event horizon and eventually, and unannounced, seize to exist at the singularity.

Well, due to tidal effects he'd be drawn out into a string of subatomic particles before reaching the singularity, but yes, basically.

I'm definitely not comfortable with the language of an object that reaches the singularity ceasing to exist, however: its mass certainly adds to the mass of a black hole, so nothing "ceases to exist". It's just that GR blows up at that point, so we can't say what's going on. And even then, GR is likely to break down significantly before reaching the singularity, so it would be foolish to take the rest of the description of what goes on in the interior too seriously anyway.

 

[Passionflower]

I'm definitely not comfortable with the language of an object that reaches the singularity ceasing to exist, however: its mass certainly adds to the mass of e a black hole, so nothing "ceases to exist". It's just that GR blows up at that point, so we can't say what's going on. And even then, GR is likely to break down significantly before reaching the singularity, so it would be foolish to take the rest of the description of what goes on in the interior too seriously anyway.

Of course nobody knows empirically what is going on inside the event horizon.

Until we have a plausible combined GR and Quantum theory that applies inside the event horizon I think it is perfectly reasonable to use GR here. By strictly using GR I am not sure what your reservation would be about 'seizing to exist'. The time-like geodesic of the object in question not longer extends past the singularity, e.g. there is no future. What else is ceasing to exist than that there exist no more future?

 

[Chalnoth]

Of course nobody knows empirically what is going on inside the event horizon.

Until we have a plausible combined GR and Quantum theory that applies inside the event horizon I think it is perfectly reasonable to use GR here. By strictly using GR I am not sure what your reservation would be about 'seizing to exist'. The time-like geodesic of the object in question not longer extends past the singularity, e.g. there is no future. What else is ceasing to exist than that there exist no more future?

It's ceasing, not seizing :P

Seizing would be capturing, like a police officer seizes a fugitive.

Anyway, with that aside, my point is merely that the effect of the mass of the object is still felt in the exterior of the black hole.

 

[heusdens]

This isn't correct. It doesn't have more mass than before. In a black hole in classical General Relativity, all of the mass is simply concentrated at the center of the black hole. It doesn't have infinite mass at all, just infinite density.

Now, we don't expect that a real black hole is actually this way. We expect quantum gravity will sort of smooth-out the singularity so that it has a large but still finite density. But we just don't yet know what the correct theory of quantum gravity is, so we can't say for certain what goes on inside a black hole.

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