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The temperature of a Schwarzschild black hole, according to Hawking, is hbar time c^3, divided by 8 π G k_{B} M. Here hbar is Planck's constant, c is the speed of light, G is Newton's constant, k_{B} is Boltzmann's constant, and M is the mass of a black hole. This gives about 6 one-hundred millionths of a Kelvin, divided by the mass of the black hole in solar mass units.

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The temperature of a Schwarzschild black hole, according to Hawking, is hbar time c^3, divided by 8 π G k_{B} M. Here hbar is Planck's constant, c is the speed of light, G is Newton's constant, k_{B} is Boltzmann's constant, and M is the mass of a black hole. This gives about 6 one-hundred millionths of a Kelvin, divided by the mass of the black hole in solar mass units.
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Robert McNees (mcnees@mastodon.social)'s status on Sunday, 08-Jan-2023 20:26:55 UTC Robert McNees
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The temperature of a Schwarzschild black hole is inversely proportional to its radius and hence inversely proportional to its mass.
Various factors of fundamental constants, along with the large mass, mean that the temperature of an astrophysical black hole is phenomenally small.
A 20 solar mass black hole, comparable to some of the black holes involved in mergers detected by LIGO, would have a temperature of around 3 x 10⁻⁹ K.

In conversation Sunday, 08-Jan-2023 20:26:55 UTC from mastodon.social permalink