Can information escape a blackhole?

[ian_dsouza]

Hello everybody, this is my first post to the forum. I am trying to learn concepts in physics at the moment.

According to the theory, the concentrated mass of a black hole warps space-time so much, that not even light can escape the event horizon.

I have a thought experiment. Say, half the mass of a black hole "instantaneously vanishes". According to general relativity, the nature of warp of the space-time surrounding the event horizon should change because of the new mass, giving rise to a gravitational wave at the instant of the change in mass.

What bothers me here is that a change in the interior of the black hole can effect the space-time outside the event horizon. This would require a transfer of infomration form the interior to the surrounding space. Since, even information cannot travel faster than the speed of light, I struggle to see how space-time outside the event horizon could be effected by such a change.

I understand that this is a thought experiment and am open to the validity of the instantaneous change in mass being questioned. It was intended along the lines of 'If the Sun disappears, the Earth would still continue to orbit for 500 seconds before it is cast into a tangential trajectory'

 

[PeterDonis]

Say, half the mass of a black hole "instantaneously vanishes".

This would violate the laws of general relativity, so there's no point in asking what GR says about it. It would be like asking what arithmetic tells you if 2 + 2 = 5.

According to general relativity, the nature of warp of the space-time surrounding the event horizon should change because of the new mass, giving rise to a gravitational wave at the instant of the change in mass.

No, according to GR this can't happen in the first place. See above.

What bothers me here is that a change in the interior of the black hole can effect the space-time outside the event horizon.

It can't. (At least, not classically; quantum effects might change this, but GR is not a quantum theory.) Your scenario can't happen in the first place. See above.

I understand that this is a thought experiment and am open to the validity of the instantaneous change in mass being questioned. It was intended along the lines of 'If the Sun disappears, the Earth would still continue to orbit for 500 seconds before it is cast into a tangential trajectory'

The latter thought experiment indeed has the same problem: the scenario is not consistent with GR, so there's no point in asking what GR says about it.

 

[ian_dsouza]

Hi PeterDonis, thanks for the quick reply. I'm still learning general relativity. Is there a specific aspect of General Relativity that is in violation here? Or is it because that in order for mass to decrease, something else must happen, like anhilation of mass to energy, which would result in a more complicated scenario.

Any input is much appreciated.

 

[WannabeNewton]

Is there a specific aspect of General Relativity that is in violation here?

Hi there Ian! What's being violated here is local conservation of mass-energy.

 

[ian_dsouza]

Hi WannabeNewton, is it posssible to have mass converted to energy within the black hole. For example, if you send in a large mass of hydrogen into a newly formed black hole, would it be plausible to have hydrogen eventually fuse to helium and possibly beyond, resulting in a release of energy and equivalent decrease in mass. Alternatively, you could send matter (e.g., a stream of Electrons) into a blakchole and successively send in the corresponding anti matter (e.g., a stream of Positrons). If you wait long enough, would it be plausible to have anhilation of mass to energy, resulting in a decrease in the black hole's mass? Does the nature of space-time inside the black hole allow the above two possibilities or other mass anhilation methods?

The reason I go into these scenarios is to understand the issue of information exchange from inside a black hole to the surroundings.

Many thanks!

 

[PeterDonis]

is it posssible to have mass converted to energy within the black hole.

Yes, but that won't change the total mass of the black hole as seen from outside. See below.

For example, if you send in a large mass of hydrogen into a newly formed black hole, would it be plausible to have hydrogen eventually fuse to helium and possibly beyond, resulting in a release of energy and equivalent decrease in mass.

This will decrease the mass of the matter (helium vs. hydrogen), but the energy released is still trapped inside the black hole, so it still contributes the same amount to the black hole's mass as seen from outside. Remember that mass and energy are equivalent.

Alternatively, you could send matter (e.g., a stream of Electrons) into a blakchole and successively send in the corresponding anti matter (e.g., a stream of Positrons).

Antimatter still has positive mass and energy; the mass of the hole as seen from outside will still be the sum of the mass and energy of everything you put into it.

The reason I go into these scenarios is to understand the issue of information exchange from inside a black hole to the surroundings.

Classically, information can only go into a black hole; it can't come out.

 

[WannabeNewton]

It seems to me what you're basically asking about is energy extraction from a black hole. This is definitely possible using both waves and massive particles when we have a rotating black hole.

See here: http://en.wikipedia.org/wiki/Penrose_process
and here: http://en.wikipedia.org/wiki/Superradiance

 

[PeterDonis]

It seems to me what you're basically asking about is energy extraction from a black hole. This is definitely possible using both waves and massive particles when we have a rotating black hole.

This is a good point, but it's important to note that none of these processes involve matter or radiation escaping from inside the hole.

 

[Nugatory]

Hi WannabeNewton, is it posssible to have mass converted to energy within the black hole.

You can convert mass to energy (and back again) just about anywhere - but the total mass of the system doesn't change unless the energy somehow leaves the system. You can think of the energy has having mass, given by Einstein's $E=mc^2$, if you want.

 

[mapsread]

One of the very defining characteristics of a black hole is its mass, and all the laws of nature appear to be set up to prevent what you are suggesting -- that the mass move away from the black hole (quickly. That is, in some manner other than Hawking radiation). It's not an experimental question and is similar to asking what happens if there are perpetual motion machines or objects moving faster than light?

Besides, information can get out of a black hole.

 

[PeterDonis]

Besides, information can get out of a black hole.

How? Remember we're talking about a classical black hole (at least, I assume that was the OP's intent), so Hawking radiation, which is a quantum effect, is not being considered.

 

[mapsread]

How? Remember we're talking about a classical black hole (at least, I assume that was the OP's intent), so Hawking radiation, which is a quantum effect, is not being considered.

Yes, Hawking radiation is what I was referring to. I forgot which forum I was in.

 

[bahamagreen]

What if you have a machine that is composed of two large masses on a pole (like a weight lifting barbell) with a controller in the center that can move the masses closer to the center or further apart.

If the controller uses a binary code of close=1 apart=0 to provide a running commentary, or just "yes/no" to a list of preset observation questions, is the change in distance between the masses detectable from outside the EH after the machine enters the EH?

Generally, does the distribution of mass between the EH and the singularity effect the gravitational field outside the EH?

 

[Chronos]

The gravitational field is always assumed to originate from the center of mass. Mass distribution is irrelevant. That might look very weird on earth. If the center of mass was not close its geometrical center all sorts of weird things would happen. A black hole has no physical geometry in this sense, so, the EH is always determined by the center of mass.

 

[WannabeNewton]

Generally, does the distribution of mass between the EH and the singularity effect the gravitational field outside the EH?

See here: http://en.wikipedia.org/wiki/No_hair_theorem