Black Hole Property Calculator

Calculate physical properties of Schwarzschild, Kerr, and Kerr-Newman black holes.

Input Parameters

Mass (Solar Masses M☉):

0.1 M☉1.0 M☉100 M☉

Spin Parameter (a/M): Schwarzschild

0 (non-rotating)0.0001 (extremal)

Charge Parameter (Q/M): Uncharged

0 (uncharged)0.0001 (extremal)

Key Equations

Schwarzschild Radius

$$r_s = \frac{2GM}{c^2}$$

Kerr Black Hole Horizons

$$r_\pm = \frac{GM}{c^2}\left(1 \pm \sqrt{1 - \frac{a^2c^2}{G^2M^2} - \frac{Q^2}{M^2}}\right)$$

Hawking Temperature

$$T_H = \frac{\hbar c^3}{8\pi GMk_B} = \frac{\hbar c}{4\pi k_Br_s}$$

Bekenstein-Hawking Entropy

$$S = \frac{k_BAc^3}{4\hbar G} = \frac{k_BA}{4\ell_P^2}$$

Evaporation Time

$$t_{\text{evap}} = \frac{5120\pi G^2M^3}{\hbar c^4} \propto M^3$$

ISCO Radius (Kerr)

$$r_{\text{ISCO}} = \frac{GM}{c^2}\left(3 + Z_2 - \sqrt{(3-Z_1)(3+Z_1+2Z_2)}\right)$$

where $Z_1 = 1 + (1-a^2/M^2)^{1/3}[(1+a/M)^{1/3} + (1-a/M)^{1/3}]$ and $Z_2 = \sqrt{3a^2/M^2 + Z_1^2}$

Physical Interpretation

Event Horizon

The boundary beyond which nothing, not even light, can escape. For rotating (Kerr) and charged (Reissner-Nordström) black holes, there are two horizons: outer and inner.

Hawking Radiation

Quantum effects cause black holes to emit thermal radiation. Smaller black holes are hotter and evaporate faster. A solar mass black hole has temperature ~60 nanokelvin!

Entropy

Black holes have enormous entropy proportional to their horizon area. This connects thermodynamics, quantum mechanics, and gravity in a profound way.

Ergosphere (Rotating BHs)

The region outside the event horizon where spacetime is dragged along with the rotation. Energy can be extracted from rotating black holes via the Penrose process.

ISCO

The innermost stable circular orbit. Objects can orbit stably outside this radius but will plunge into the black hole inside it. For accretion disks, this determines the inner edge.