Final answer:
A black hole will evaporate if it emits more energy through Hawking radiation than it gains from mass accretion, resulting in its event horizon shrinking and the black hole's eventual disappearance.
Step-by-step explanation:
When a black hole emits energy more quickly through Hawking radiation than it gains mass from accretion, the black hole will evaporate. This process occurs when energy in the form of particle-antiparticle pairs is emitted just outside the event horizon of the black hole. One of the particles falls into the black hole while the other escapes, leading to a net loss of mass for the black hole.
As the black hole loses energy and, consequently, rest mass, its event horizon shrinks, enhancing its gravitational field and thereby increasing the rate of pair production. This feedback loop results in an exponential increase in the process, culminating in the black hole shrinking away, until it finally disappears altogether in a burst of particles and gamma rays.