# Are black hole event horizons hotter than our Sun?

The outside (not inside) of black holes, the event horizon, are apparently extremely hot, and get even hotter the smaller in size and mass they are. Being completely black, are they generally more hotter than normal stars? Are black holes hotter than our sun?

An in-detail comparison of their heat and the heat of the sun would be appreciated, if not only temperature but electromagnetic radiation measurements.

• Black holes are apparently extremely hot. What did you read or watch that made you think this? Oct 30, 2022 at 3:20
• Wikipedia: A black hole of one solar mass has a temperature of only 60 nanokelvins. Oct 30, 2022 at 3:22
• Are you perhaps referring to the accretion disk getting hot? That's a very different thing, do you want to edit the question after you've done some rethinking? Oct 30, 2022 at 3:37
• Here is a hypothetical black hole as hot as our Sun: physics.stackexchange.com/q/362721 Oct 30, 2022 at 6:25
• This question should be reopened - for a hypothetical static observer hovering near the horizon, the Hawking radiation may indeed appear hotter than the Sun. Oct 31, 2022 at 19:43

Heat in black holes is due to Hawking radiation, which means in particular that the temperature you measure will depend on the observer you are considering. For an observer at infinity, the temperature is given by the Hawking temperature, $$T_H = \frac{\hbar c^3}{8\pi k_B G M}.$$ Or, in units with $$\hbar = c = G = k_B = 1$$, $$T_H = \frac{1}{8\pi M}.$$ However, this is the temperature measured by static observers at infinity. In other words, it is the temperature that observers at a fixed, infinite "radial distance" to the center of the black hole measure. Other observers measure other temperatures. If you are free falling, you won't measure any temperature at all: it is $$T = 0 \text{K}$$. If you are at a fixed, finite radial distance $$r$$, then the temperature is $$T_H = \frac{1}{8\pi M \sqrt{1 - \frac{2 M}{r}}}.$$ Notice that $$r \to +\infty$$ recovers the previous formula. Furthermore, for $$r \to 2M$$ (i.e., close to the horizon), the temperature gets arbitrarily large. Hence, yes, the black hole will be hotter than the Sun if you are hovering sufficiently close to it. Furthermore, there is no limit on the black hole's mass: this will be true for a black hole of any size, as long as you are close enough.