Does the Total Energy of a Black Hole Change During Evaporation?

[DrZoidberg]

Hi,
the gravitational field around a black hole is a form of negative energy. When a black hole evaporates it is converted into photons. These photons move away from the black hole. After it evaporated the gravitational field is gone so the negative energy is gone. But the total amount of energy stays the same because the total energy of all the photons is smaller than the mass of the black hole originally was.
How much of the positive energy of a black hole disappears when it evaporates? Does it depend on it's mass? Could a black hole in theory be so massive that nearly all it's energy disappears? In other words, can it be so massive that the positive energy (it's mass) is identical to the negative energy of it's gravitational field?

 

[Drakkith]

I don't believe any energy is lost or gained in the lifecycle of a black hole. Anything caught in the black hole would gain energy on the way in, and lose that energy on the way out. However, I don't know for sure.

 

[clamtrox]

Hi,
the gravitational field around a black hole is a form of negative energy. When a black hole evaporates it is converted into photons. These photons move away from the black hole. After it evaporated the gravitational field is gone so the negative energy is gone. But the total amount of energy stays the same because the total energy of all the photons is smaller than the mass of the black hole originally was.
How much of the positive energy of a black hole disappears when it evaporates? Does it depend on it's mass? Could a black hole in theory be so massive that nearly all it's energy disappears? In other words, can it be so massive that the positive energy (it's mass) is identical to the negative energy of it's gravitational field?

Why do you think the endstate has zero gravitational potential energy? It seems reasonable to say that the endstate is somehow less bound than the black hole, but that does not mean the gravitational energy is smaller; you need to take into account expansion of the universe and all that.

To be even more sneaky, why do you think black holes have energy in the first place? The solution is entirely vacuum: you have something in the singularity, but that region is not described by GR.

 

[Chronos]

The mass of a black hole constitutes positive energy, which is exactly offset by the negative energy of its gravity, so there is no missing, or excess energy when a black hole evaporates.