# How can a black hole evaporate instantly if speed of gravity is c?

1. Jan 17, 2012

### kamenjar

How can a black hole evaporate "instantly" if speed of gravity is c?

Hi all,

This question has been baffling me for quite some time...

Let's say that a tiny black hole is already formed and an observer at some short/safe distance away from it is observing it. The observer sees a flashlight near the event horizon that is 10 billion light years away when measured by the observer due to bending of spacetime.

Now the black hole does evaporate very fast form its own frame of reference, but it should take very long time for that change to be observed (felt) in the reference frame of the observer, right? Gravity waves propagate at speed of light, so at that far displacement it would take more than 10 billion years for the observer to see the black hole evaporate.

Is there something wrong with this logic? I read stories about creating experimental mini black holes on earth that will evaporate etc, and it doesn't make sense to me.

By the way, I am just a SW Engineer that understands some GR principles, so formulas would be an overkill :)

2. Jan 17, 2012

### alexg

Re: How can a black hole evaporate "instantly" if speed of gravity is c?

Are you saying that the observer is 10 billion lys away from the black hole?

3. Jan 17, 2012

### kamenjar

Re: How can a black hole evaporate "instantly" if speed of gravity is c?

The observer is at a small "safe" distance (measured probalby in thousands or millions of KM) from the black hole when we "place" the black hole in our space and measure where it would be, however (unless I am understanding this wrong) the objects near the event horizon appear billions of light years distant and displaced in space. In other words, if the flashlight wanted to reach the observer, it would take it billions of years of travel at speed c.

Edit: My understanding is that the gravity of the black hole in fact "extends" the space of a few million square KM into additional infinite amount of spacetime towards it.

4. Jan 17, 2012

### twitch1

Re: How can a black hole evaporate "instantly" if speed of gravity is c?

Ive heard that objects at the event horizon appear to be at rest once they reach the event horizon to the distant observer, even though the object being viewed has actually gone over the event horizon and into the black hole.

5. Jan 17, 2012

### kamenjar

Re: How can a black hole evaporate "instantly" if speed of gravity is c?

Quite correct.

Let's say for the sake of this experiment that the flashlight changed its mind at the last instant before reaching the EH and decided to accelerate to c instantly and start traveling towards the observer and away from the black hole that just evaporated as the flashlight took off. My understanding is that even the flashlight would experience tremendous gravity along the way (though the BH already evaporated). Change in gravity is following the flashlight at speed c just behind the flashlight itself.

6. Jan 17, 2012

### twitch1

Re: How can a black hole evaporate "instantly" if speed of gravity is c?

I can see your point. Though the source of the gravitational force has ceased to exist, the force that was exerted while it still existed is still traveling outward in all directions at the speed of light(think if you blink a flashlight, the waves or particles that were emitted dont cease to exist though the source was turned off, they continue on in the direction they were emitted). The flashlight would never be free of that gravitational force since they are traveling together at the same speed and left at the same time. Now, the flashlight couldnt just stop, it would have to change direction instantly and in the opposite direction of the gravitational force in order to become free of it?

7. Jan 17, 2012

### kamenjar

Re: How can a black hole evaporate "instantly" if speed of gravity is c?

And huge energy burst etc. but theoretically even this case makes it weirder... I wonder when will the flashlight and the observer "meet" if the flashlight was to turn around...

But aside from this new scenario, unless there are other rules in GR, the observer would still have to wait more than 10 billion years to grab the flashlight, which means that the effect of the black hole has not dissapeared, which means that it in fact did not evaporate in our time frame, which means that it is very unsafe to play with fire and micro black holes and try to create micro black holes. Imagine if such manmade black hole was to "fall thru earth".

Check Paragraph: Manmade micro black holes

8. Jan 17, 2012

### twitch1

Re: How can a black hole evaporate "instantly" if speed of gravity is c?

Considering that even the smallest black hole would be sufficient to suck in our planet, and almost everything in the vicinity, I dont see how you could create one and not get "burned". If nothing can escape a black hole, then that goes for any kind of containment implementation.

9. Jan 17, 2012

### alexg

Re: How can a black hole evaporate "instantly" if speed of gravity is c?

I don't see how you can conclude this. The observer can measure how far he is from the event horizon, and thus how far he is from the flashlight. Gravity warps the geodesic, not the distance.

10. Jan 17, 2012

### Staff: Mentor

Re: How can a black hole evaporate "instantly" if speed of gravity is c?

This entry in Ted Bunn's Black Hole FAQ is relevant:

http://cosmology.berkeley.edu/Education/BHfaq.html#q9

The whole FAQ is worth reading, but I linked to the particular question/answer that is most relevant to the OP.

Another point is also worth noting: the space (or spacetime) near the black hole horizon is *not* "infinitely stretched":

This is not correct. The space is somewhat "stretched" by the presence of the hole, relative to the imagined "flat background before the hole is put in", but even that statement is somewhat misleading; for one thing, it's observer dependent; observers "hovering" at a constant radial coordinate above the hole see space as "stretched", but observers freely falling into the hole do not. (There are also technical issues with trying to actually consistently model the relationship between the space as it "would have been" without the hole, and the space as it actually is in the presence of the hole.)

What *is* true is that, if the "flashlight" is placed closer and closer to the hole's horizon and "hovers" there, the outgoing light beam it emits will take longer and longer to reach an observer "hovering" at a very, very large radial coordinate. However, that delay is not due to the curvature of space by itself; it's due to the curvature of *spacetime*, which includes time as well as space. A better way to think about what's happening may be this: if we draw a spacetime diagram of a small "patch" of spacetime very far away from the hole, outgoing light rays travel on 45-degree lines. However, if we move our small "patch" of spacetime closer and closer to the hole, the worldlines of outgoing light rays get tilted inward more and more, until *at* the horizon, they are vertical--that is, an "outgoing" light ray at the horizon stays at the horizon forever. So the reason the outgoing light is delayed is that the light cones are tilted inward.

This picture should also help in understanding what Ted Bunn's FAQ answer is talking about. As the black hole evaporates, its mass decreases, meaning that the tilting of the light cones at a given physical distance away from the hole gets gentler. This means that the light isn't delayed as much; and finally, when the hole evaporates completely, the light cone tilting is completely gone as well. So as the hole evaporates, outgoing light from the "flashlight" is delayed less and less. (The stretching of space, as seen by "hovering" observers, also gets less and less as the hole evaporates.)

11. Jan 17, 2012

### alexg

Re: How can a black hole evaporate "instantly" if speed of gravity is c?

The smaller the black hole, the faster it evaporates into a burst of gamma rays.

Remember too that gravity drops off as the square of distance, and microblack holes are just that, micro.

12. Jan 17, 2012

### kamenjar

Re: How can a black hole evaporate "instantly" if speed of gravity is c?

.. which means that it warps spacetime, which means that warps space and time but it does not mean that 10 bil LY distant? What's the difference? How would the observer know if he lived in a basement with no windows and only a telescope with a view covering only the flashlight?

13. Jan 17, 2012

### twitch1

Re: How can a black hole evaporate "instantly" if speed of gravity is c?

Ok, was talking out my rear again. Yeah, forgot about the square of distance thing, and was a little confused as to what exactly micro would be. Was thinking micro in the grand scheme of things considering most black holes are rather immense. I guess in this case you could say pico. Even pico though, it would still be a darn dangerous thing to be playing with. In order for the hole to form, you would have to have something of immense density and mass collapse on its self. Would that even be possible on a scale that small? Or a small scale period? Thats a lot of matter. And in the event that the pico black hole began to take on more and more matter, wouldnt you end up with a snow ball effect that results in a normal size black hole, or is there a limit proportional to the initial size of the black hole?

14. Jan 17, 2012

### alexg

Re: How can a black hole evaporate "instantly" if speed of gravity is c?

Only a telescope? Let's at least give him a spectrograph as well. Then he could calculate the red shift and see if it was attributable to cosmological expansion, or if the value of the red shift matched what would be produced by an intense gravity field.

BTW, if there are no windows, how does the telescope have a view?

15. Jan 17, 2012

### kamenjar

Re: How can a black hole evaporate "instantly" if speed of gravity is c?

Thaks a lot for the lengthy answer. I did read the faq a while back and I think that I do understand anything that you and the rest of the forum members are explaining to me.

The part that I don't get though is this change of mass propagating instantly (c) and instantly "straightening" the geodesics. From a reference frame of the black hole itself, yes, but from the observer that is say 1m from the pico black hole, I don't see how this information can reach him in an "instant". I would figure it would take eternity for the effect to disappear.

16. Jan 17, 2012

### kamenjar

Re: How can a black hole evaporate "instantly" if speed of gravity is c?

Telescope needs only a hole in the ground wide enough :)
So he has a spectrograph and measures the redshift and gets a huge Z and concludes that the flashlight is very far away, even though the pico black hole is inside the house (now I am exaggerating, but you do see my point, I hope).

17. Jan 17, 2012

### twitch1

Re: How can a black hole evaporate "instantly" if speed of gravity is c?

Im sorry if Im being a bother to anyone here, Im just trying to learn. No one I know can answer questions I have, so I decided to go this route. When I read things, it raises other questions for me. Is the sudden use of pico black hole after my post being used as sarcasm, or actually as the description I had intended?

18. Jan 17, 2012

### alexg

Re: How can a black hole evaporate "instantly" if speed of gravity is c?

I'm pretty sure that you get different values for expansion redshift and gravitational redshift. So he concludes the flashlight is down a gravity well.

19. Jan 17, 2012

### kamenjar

Re: How can a black hole evaporate "instantly" if speed of gravity is c?

Ok so he compares the magnitude of the light which is very faint due to gravitational effect and and compares to expansion of space, he concludes that the object is accelerating away from him but is still far more distant than his house.

We can drop this. Distances can be confusing if measured form different reference frames, so we can use time:
a) How long does the light from the EH inside the gravity well take to reach him?
b) How long until the observer notices that the gravitational effect of the BH has dissapeared?

I think that science answers "less than a second" to "b" but think about answer to "a".... It would mean that in case of "a" the black hole never existed. Given my limited knowledge answering "less than a second" to b) would violate some GR speed of information information rules.

So please enlighten me why isn't the answer "billions of years"? You are most likely right in all this, but I don't understand why :)

20. Jan 17, 2012

### alexg

Re: How can a black hole evaporate "instantly" if speed of gravity is c?

If the observer is 10 light seconds away from the BH, it will take him ten seconds to note that the event horizon has disappeared.

Light does not slow down, and distances do not greatly change.