Two questions about black holes...

[Beta]

I understand that black holes evaporate, and that from the point of view of a distant observer an object falling in will approach the event horizon forever, but the combination of these facts puzzles me.

1) Suppose a black hole is scheduled to evaporate in, say, 10^50 years. And suppose I fall into it. If I look up as I fall, I should be able to see as much time pass on Earth as I care to watch, before I cross the event horizon. In particular I should see the year 10^50 AD arrive on Earth. But at that point the black hole should no longer exist (and I never crossed the event horizon) so where am I?

The closest I can get to an answer is that during my fall, tidal forces will tear me into particles, all of which will eventually escape and be seen by distant observers as Hawking radiation. But this contradicts the idea that tidal forces are quite mild at the event horizon of a really big black hole. So the only way to make this solution work is to suppose that a black hole seems to evaporate very quickly from the point of view of an observer falling in, and that just doesn't sound right.

2) The usual formulation of the space-time metric of a black hole has a singularity at the center. But this is a static solution. If a big object collapses and slows down during its fall (from the point of view of a distant observer) then couldn't the metric be relatively flat in the center? I'm sure people have simulated the process of collapse, but intuitively I don't see how an object could reach the static state in a finite period of (distant) time. In distant time, when does the singularity form?

[rstevenson]

(I'm not an expert!)

My impression is that tiny black holes (on the order of 1/10th of a millimeter in size) must evaporate, but that large ones continue to gradually accumulate material -- including you, if you fall in -- and do not evaporate. Here's a relevant quote from Wikipedia's article on Black Holes ...

Stellar mass (and larger) black holes receive more mass from the cosmic microwave background than they emit through Hawking radiation and will thus grow instead of shrink.

Hope this helps with your question #1. As for #2, I will have to pass.

Rob

[makc]

#1 is easy, thanks to the notion of space-time continuum. as long as you do not cross the horizon, all the events that happen for observer on earth, also happen for you, just in different time and place. so, assuming your black hole is not the one that rstevenson say is big enough to not evaporate, i.e.

Suppose a black hole is scheduled to evaporate in, say, 10^50 years

while you watch time passing on Earth, it does evaporate behind your back, until at some point it is completely gone for both you and earth, and you are flying through empty space, away from Earth (or whatever is left from it after 10^50 years).

#2 imagine "almost" formed black hole with only thin particle layer remaining outside of critical radius sphere, then I think it would be fair to apply our "static" solution (outside, and inside up to some small depth) - which says that according to earth observer, remaining particles will cross critical radius sphere in time t=+∞ (or, if you prefer, never) but, according to someone falling with them, they will cross it in finite time

(I'm not an expert!)

ditto but these seems simple questions. as they say, "correct me if I am wrong".

[Beta]

Stellar mass (and larger) black holes receive more mass from the cosmic microwave background than they emit through Hawking radiation and will thus grow instead of shrink.

All right, so I'll put a tent around it.

[Beta]

[The black hole] does evaporate behind your back, until at some point it is completely gone for both you and earth, and you are flying through empty space, away from Earth (or whatever is left from it after 10^50 years).

1a) This applies to everything that ever fell into the black hole, all the stars and everything. If they really do all come boiling out eventually, they must be in the form of what we call Hawking radiation.

1b) This means that a big black hole evaporates really fast when you're close to it. And yet tidal forces, which I've always heard associated with Hawking evaporation, is still really weak. Something doesn't add up.

Imagine "almost" formed black hole with only thin particle layer remaining outside of critical radius sphere, then I think it would be fair to apply our "static" solution (outside, and inside up to some small depth) - which says that according to earth observer, remaining particles will cross critical radius sphere in time t=+∞...

But there's no singularity at the center, that's my point.

[makc]

And yet tidal forces... is still really weak.

Why?

[Beta]

And yet tidal forces... is still really weak.

Why?

For a static, symmetrical black hole, the tidal forces at the event horizon are proportional to 1/M^2.

[makc]

So? Here goes a funny quote from here:
[quote][quote]What would happen if you could travel at such a speed (faster than the escape velocity) as to have a stable orbit of a black hole just beyond the event horizon and you were to stick your hand inside the boundary? Would you be sucked in? Would your hand be taken but your velocity keeps you safe?[/quote]There are no orbits around the black hole (stable or otherwise) inside the photon sphere, at a schwarzschild radius of r=3M (geometric units). This is the radius at which the orbital speed around the black hole becomes equal to 'c'. Nothing can move faster than the speed of light, therefore nothing can orbit the black hole inside the photon sphere.

The event horizon itself is at a schwarzschild coordinate of r=2M (inside the photon sphere).

You need to accelerate (with a rocket engine) in order to maintain station at a constant 'r' value in the Schwarzschild coordinate system whenever you are inside the photon sphere r<3M.

The required acceleration goes to infinity as you approach the event horizon -so at some finite point short of the event horizon, you will be crushed, and your hand (if you allow it to dangle unsupported) won't be able to support it's own weight and it will be ripped off.[/quote]I don't know about you, but to me it sounds like significant tidal forces

1a) This applies to everything that ever fell into the black hole, all the stars and everything. If they really do all come boiling out eventually, they must be in the form of what we call Hawking radiation.

Again, I don't see a problem. Stuff that never crossed the horizon remains in our universe - maybe spagettified and disassembled into particles, but it's still here, so why should it disappear ? Hawking radiation probably only means that infalling matter loses its energy to it and in the end of this epic process should be very cold (bye, bye, thermodynamics).

[Beta]

You need to accelerate (with a rocket engine) in order to maintain station at a constant 'r' value in the Schwarzschild coordinate system whenever you are inside the photon sphere r<3M.

The required acceleration goes to infinity as you approach the event horizon...

I don't know about you, but to me it sounds like significant tidal forces

That's not tidal force at all.

Stuff that never crossed the horizon remains in our universe - maybe spagettified and disassembled into particles, but it's still here, so why should it disappear?

My point is that it looks as if nothing ever crosses the event horizon, which surprises me.

Hawking radiation probably only means that infalling matter loses its energy to it and in the end of this epic process should be very cold (bye, bye, thermodynamics).

I don't follow your reasoning, but the final stages of evaporation of a black hole are very hot.

[makc]

Hawking radiation probably only means that infalling matter loses its energy to it and in the end of this epic process should be very cold (bye, bye, thermodynamics).

I don't follow your reasoning, but the final stages of evaporation of a black hole are very hot.

the reasoning: imagine BH in your "tent" - nothing goes inside, but hawking radiation goes outside. in the end, BH evaporates, and whatever is left inside, has lost loads of energy through radiation. so, if conservation law holds for your "tent", whatever is inside is now much colder than it was before.

[Beta]

By that reasoning the Sun must be much colder than the gas cloud from which it formed. You are confusing temperature with energy content. (You are also assuming that my tent is opaque in only one direction, but never mind.)

[The Code]

Hawking radiation probably only means that infalling matter loses its energy to it and in the end of this epic process should be very cold (bye, bye, thermodynamics).

I don't follow your reasoning, but the final stages of evaporation of a black hole are very hot.

the reasoning: imagine BH in your "tent" - nothing goes inside, but hawking radiation goes outside. in the end, BH evaporates, and whatever is left inside, has lost loads of energy through radiation. so, if conservation law holds for your "tent", whatever is inside is now much colder than it was before.

Quote:

"Actually, the biggest black holes are the coldest because their so-called Hawking temperature is measured in billionths of a degree above absolute zero. The hottest black holes are microscopic and have less than 1 trillion grams of mass, and temperatures that increase from a million degrees to trillions of degrees as they evaporate.

Quantum black holes which have masses of 0.00001 grams have sizes equal to 10^-33 centimeters and their evaporation temperatures are 10^32 degrees, making them the hottest possible objects in the universe...if they exist".

http://www.astronomycafe.net/qadir/q2973.html

Mark

[The Code]

And just for the record, As i got closer and closer to the black hole, measured in light years, What would happen to my Body Clock? Would my body stop functioning, long before the Event Horizon?

Mark

[Beta]

As I got closer and closer to the black hole... what would happen to my Body Clock?

You should probably get a firm grip on Special Relativity before you try General.

[The Code]

As I got closer and closer to the black hole... what would happen to my Body Clock?

You should probably get a firm grip on Special Relativity before you try General.

I feel that hurt.

Never mind, maybe in another universe, they maybe have Hot Black Holes. Job done Yeah?

[makc]

By that reasoning the Sun must be much colder than the gas cloud from which it formed.

what can I say to that, good point Still, can we imagine a BH made from some neutral particles soup that does not launch any kind of chain reactions when compressed? And then let's drop same neutral matter onto this BH.

[Beta]

I feel that hurt.

Uh... If you mean I offended you, I apologize, I wasn't trying to be patronizing. It's just that the idea of reference frames is pretty slippery. They're not intuitive, it takes a while to understand them, and it really pays to start with the simple cases.

[The Code]

I feel that hurt.

Uh... If you mean I offended you, I apologize, I wasn't trying to be patronizing. It's just that the idea of reference frames is pretty slippery. They're not intuitive, it takes a while to understand them, and it really pays to start with the simple cases.

No need. If it was possible to, As you say, "Fall into it" You would see the outside universe on fast forward (Time) depending on the size of the black hole. Here's a question for you. How old is the universe, that an 18 billion solar mass black hole can see?

what can I say to that, good point Still, can we imagine a BH made from some neutral particles soup that does not launch any kind of chain reactions when compressed? And then let's drop same neutral matter onto this BH.

Until the big crunch?

[Chris Peterson]

And just for the record, As i got closer and closer to the black hole, measured in light years, What would happen to my Body Clock? Would my body stop functioning, long before the Event Horizon?

Absolutely nothing would happen. Your body clock would keep right on at the same rate as always (as seen from your own frame of reference). It would be different from other clocks in other frames of reference, of course. But that would have no impact on you. As you fell toward the black hole, everything would continue to seem normal to you, even as you fell through the event horizon.

[Chris Peterson]

How old is the universe, that an 18 billion solar mass black hole can see?

The Universe is 13.75 billion years, with an uncertainty of less than 200 million years.

A supermassive black hole such as you describe can form in anywhere from nearly instantly to a few hundred million years, depending on just when in the evolution of the Universe it occurred, and what the local mass density was. The existence of such objects is irrelevant to discussions of the age of the Universe.

Until the big crunch?

Theory and observation strongly argue against the possibility of a big crunch ever occurring.

[astrolabe]

Hello Beta

By that reasoning the Sun must be much colder than the gas cloud from which it formed.

Yes.

[alter-ego]

As I got closer and closer to the black hole... what would happen to my Body Clock?

You should probably get a firm grip on Special Relativity before you try General.

Hello Beta -
Certainly it is more helpful the more familiar you are with SR and GR, but Mark's question is relatively easy to answer. Assuming that you are approaching a "dead" black hole (no accretion disk, no charge, no magnetic fields/non-rotating), in your reference frame you won't shut down until until differential accelaration (tidal force) rips (or noodles) you to death. In your frame of reference, everything is cool , your body clock tics as normal. But what about the Event Horizon? If you were approaching a solar-mass black hole, you wouldn't make it to the EH . But thankfully, you are heading toward a super-massive BH . For these behemoths, the differential acceleration is much less at the EH, so you slip right on in, checkin' out the odd-ball, probably distorted views. For a 1000,000 solar-mass BH, you would have ~6 sec to enjoy life after crossing the EH .

FYI, I'm comfortable with SR, and can talk some about GR, but I'm far from an expert. I lose it at the tensors...

Last comments: Clearly no one really knows what physics really lies on the other side of an EH. Period. The discussion about not being ripped apart approaching the EH boundary is realistic. Calculations predicting acceleration past the EH assumes a singularity, and this is where I will share with you my opinion. I believe that the next significant breakthroughs will incorporate quantum theory into gravitation theory. This, by itself, is not a new thought, but I have high expectations that the fundamental point-source limits which result in infinite densities, infinite energies, and infinite times will go away in the same manner as the "UV Catastrophe" went away with Quantum Theory. This is just what I think, and only that - I'm don't care to convince anyone else. One can speculate on other ramifications, but I'm not. Sure it's fun to banter about this stuff, but ultimately, beliefs are argued and discussions become circular and not enjoyable any more. But one thing will be true: GR will be a direct fallout of whatever follows next - just as Newtonian Mechanics falls out of GR. We haven't found a robust alternate theory to GR yet, but it will come.

As far as a frame of reference goes, you truly only have one - yours.