Where does the matter/energy go when a black hole evaporates?

[garytse86]

The first law only applies if the system is isolated, i.e. it cannot lose energy to surroundings. How then, is the total amount of energy in the universe constant?

When black holes suck in matter, you could argue that the information is still in the black hole, but black holes do evaporate, where does the matter/energy go when the black hole has evaporated? Does it mean energy is not really conserved?

Gary

 

[da_willem]

The first law (of thermodynamics) includes a term Q for the heat exchange with the surroundings. This makes it also applicable to non-isolated systems.

Furthermore, when a black hole evaporates, it does so by radiating energy. This radiation is called Hawking-radiation after Stephen Hawking who first predicted it's existence, and can be explained using quantum mechanics.

So by the time the black hole has totally evaporated, it retrieved all its energy to the universe. So energy/mass conservation still holds...

 

[russ_watters]

Black holes are in the universe. Whether what is behind the event horizon is really part of the observable universe or not is a little bit semantic: a black hole has mass and mass is equivalent to energy. The energy is still in the universe.

When a black hole evaporates, the energy just dissipates into the universe.

 

[garytse86]

oh I thought the black hole would evaporate completely before emitting all the radiation back into the universe.

Anyway how does the radiation get out of a black hole?

 

[da_willem]

How can a black hole radiate? It sounds bizarre, considering that nothing, even light can escape from the gravitational pull of a black hole. It's a quantum mechanical (QM) effect first described by Stephen Hawking. The explanation I can give you is probably too simplistic but I think it'll ease your mind...

As predicted by QM the vacuum of space is a whirl of particles. These particles are created accompanied by its anti-particle (so not violating any preservation laws except for temporarily 'lending' some energy) and directly annihalated in a time allowed by the Heisenberg uncertainty principle.

When this proces of creation of particles happens near the event-horizon of a black hole, one of the particles can escape while the other falls into the black hole. So this escaping particle seems to the outside world as coming from the black hole. This is called Hawking radiation.

There is a bit of an energy problem though. The 'lend' energy must be repaid by the black hole. That's why the black hole loses energy and eventually totally evaporates.

Again, the truth is probably far more complex but I think it's a quite satisfactory explanation.

 

[russ_watters]

Originally posted by garytse86
oh I thought the black hole would evaporate completely before emitting all the radiation back into the universe.

Anyway how does the radiation get out of a black hole?

I think you're missing something key here. Your first and second sentences are talking about exactly the same thing, they are not separate issues:

A black hole evaporates by radiating its energy back into the universe.

 

[garytse86]

but how do you know the black hole would not evaporate completely before emitting all the radiation?

 

[russ_watters]

Originally posted by garytse86
but how do you know the black hole would not evaporate completely before emitting all the radiation?

Again, you have two identical concepts that you are separating. Combine them:

A black hole evaporates because it is emitting radiation. Or put another way, the act of emitting the radiation is the evaporation. Since matter=energy, all of the mass of the black hole is lost as radiation.

Or: if you have a 1 gallon bucket and you pour 1 gallon of water out of it, is the bucket empty?

Or: if you have a 1 gallon bucket and its full, then you pour all the water out of it, how much water did you pour out?