The formula for the Bekenstein-Hawking entropy of a Schwarzschild black hole, with numerical values plugged in. The entropy is about 10^{77} times Boltzmann's constant, times the square of the mass of the black hole in solar mass units.

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1. Robert McNees (mcnees@mastodon.social)'s status on Sunday, 08-Jan-2023 20:35:06 UTC Robert McNees

   in reply to

   What does this mean for the entropy?

   The area of the Schwarzschild horizon is 4π times its radius squared. And the Planck length is astonishingly small – about 1.6 x 10⁻³⁴ meters. So the entropy of a 20 solar mass black hole is about 4 x 10⁷⁹ k_B.

   This is many orders of magnitude larger than a self-gravitating ball of hot gas with comparable mass.

   Black holes are far and away the most entropic objects in the Universe. Most of the entropy in the Universe is in the form of black holes.