How is Hawking radiation related to black hole mass?

• A. Temperature is inversely proportional to mass; smaller black holes are hotter.
• B. Temperature increases with mass.
• C. Temperature is independent of mass.
• D. Temperature is proportional to mass squared.

Answer: (A)

Hawking radiation gives black holes a temperature that falls as their mass grows. The temperature scales roughly as one over the mass, so smaller black holes are hotter. This comes from quantum effects near the event horizon: particle-antiparticle pairs form, and one member can escape as radiation while the other is trapped, producing a steady glow whose temperature depends on how strong gravity is at the horizon. Since smaller mass means a stronger gravitational field at the horizon, the resulting radiation is hotter. As the hole emits radiation and loses mass, its temperature rises further, speeding up evaporation. So the idea that temperature is inversely related to mass is the correct description. The other possibilities—temperature increasing with mass, being independent of mass, or growing with mass squared—don’t align with Hawking’s result.