Black Hole Thermodynamics

Hawking radiation, entropy, and evaporation

T_H (nK)
S/k_B
r_s (km)
L_H (W)
Hawking temperature (1974) is the temperature at which a black hole radiates as a blackbody:
T_H = ℏc³ / (8πGMk_B) ≈ 6.17×10⁻⁸ K · (M☉/M)
Bekenstein-Hawking entropy: S = k_B A/(4ℓ_P²) — area in Planck units, a profound link between gravity and thermodynamics. Evaporation time: τ ∝ M³ — a solar-mass BH evaporates in ~2×10⁶⁷ years. For a Kerr BH, the horizon area A = 8πGM[M + √(M²−a²)]/c², reducing T_H. The four laws of BH mechanics mirror ordinary thermodynamics exactly.