Bekenstein-Hawking Black Hole Entropy

A black hole's entropy is proportional to its event horizon area: S = kc³A/(4Gℏ) = A/(4ℓ_P²). This profound result, connecting thermodynamics, gravity, and quantum mechanics, suggests that information is encoded on the 2D horizon — the holographic principle. Hawking radiation causes slow evaporation at temperature T = ℏc³/(8πGMk).

Mass Muser input × M☉
Schwarzschild radius r_s2GM/c²
Horizon area A4πr_s²
BH Entropy Skc³A/(4Gℏ) = A/4 in Planck units
Hawking Temperature T_Hℏc³/(8πGMk)
Evaporation time τ5120πG²M³/(ℏc⁴)