🕳️ General Relativity & Black Hole Thermodynamics
Schwarzschild Radius & Black Hole Calculator
Compute the gravitational event horizon radius ($r_s = \frac{2GM}{c^2}$), photon sphere radius ($1.5 r_s$), Hawking radiation temperature ($T_H$), and Bekenstein-Hawking entropy.
🌍 Earth ($r_s = 8.87\text{ mm}$)
☀️ Sun ($r_s = 2.95\text{ km}$)
⭐ Cygnus X-1 (21 M☉)
🌌 Sagittarius A* (4.15M M☉)
🌀 M87* Supermassive (6.5B M☉)
Mass Input
Event Horizon Radius (r_s)
2.954 km
Photon Sphere ($1.5 r_s$)
4.431 km
Hawking Temp ($T_H$)
6.17 × 10⁻⁸ K
Bekenstein Entropy
1.05 × 10⁷⁷ J/K
💡 Schwarzschild Metric Solution:
$$r_s = \frac{2 G M}{c^2} = \frac{2(6.6743 \times 10^{-11})(1.989 \times 10^{30})}{(2.9979 \times 10^8)^2} = 2,954\text{ m}$$
General Relativity & Black Hole Mechanics
Karl Schwarzschild solved Einstein's field equations for a spherically symmetric vacuum mass in 1916:
- Schwarzschild Radius (Event Horizon): $$r_s = \frac{2GM}{c^2}$$
- Photon Sphere (Unstable Light Orbit): $$r_{\text{ph}} = \frac{3}{2} r_s = \frac{3GM}{c^2}$$
- Hawking Radiation Temperature: $$T_H = \frac{\hbar c^3}{8\pi G M k_B}$$
- Bekenstein-Hawking Entropy: $$S = \frac{k_B c^3 A}{4 G \hbar} \quad (A = 4\pi r_s^2)$$