Black Hole
Reference: r_s ≈ 2.95 km × M/M☉. Stellar BHs evaporate vastly slower than the age of the universe (~4×10¹⁷ s). A 10¹² kg primordial BH evaporates in ~13 Gyr — comparable to the universe’s age.
About this tool
Schwarzschild (non-rotating, uncharged) black hole. Pick any mass in solar / Earth / kilogram units; everything is derived.
- r_s = 2GM/c² ≈ 2.95 km × M/M☉ — the event horizon radius.
- T_H = ℏc³/(8π·GM·k_B) — Hawking temperature.
- L = ℏc⁶/(15360π·G²M²) — Hawking luminosity.
- τ = 5120π·G²M³/(ℏc⁴) — evaporation lifetime (no infall).
- S = (k_B π r_s² c³)/(ℏG) — Bekenstein-Hawking entropy.
Notes
Stellar-mass BHs are extremely cold (T_H < μK) and effectively never evaporate. A primordial BH of ~10¹² kg has τ comparable to the age of the universe. Effective density M / (⁴⁄₃π r_s³) falls as 1/M²: super-massive BHs have lower-than-water effective density.