I have not directly studied Hauwking's radiation, I only know what my teachers told me about it and which is constantly repeated in popular science texts.
It says: If a pair of virtual particles materializes on the black hole's event horizon, one of them may move away, while the other falls into the hole, so that the black hole emits a radiation and gradually evaporates.
I don't understand this evaporation process as in the process the black hole gains a particle, so that its mass increases instead of decreasing. Worse, the universe outside the hole is also gaining mass to the detriment of the void.
Could somebody help?