Final answer:
When the mass of a black hole doubles, its temperature halves due to the inverse relationship between mass and temperature inherent in Hawking radiation.
Step-by-step explanation:
When a black hole increases in mass by a factor of two, its temperature decreases proportionally. Specifically, the temperature of a black hole is inversely proportional to its mass, according to the principles of Hawking radiation. Therefore, if the mass of a black hole doubles, its temperature will halve. As such, the correct answer to the question is b) It halves.
For example, if you had a black hole that was initially at temperature T, after the mass doubles, the new temperature would be T/2. This counterintuitive result arises from the nature of black holes and quantum effects, and it reflects the concept that as black holes become more massive, they actually become cooler.