See also: Black hole (homonymy)

Notations

• has the surface of the surface of the sphere contained in the horizon of the events of the black hole,

• T the temperature in Kelvin,
• C the speed of light,
• $\{\backslash \; hbar\}$ the reduced constant of Planck, $\backslash \; hbar\; =\; \{H\; \backslash \; over\; 2\; \backslash \; pi\}$,
• K the Boltzmann constant,
• G the universal constant of gravitation,
• M the mass of the black hole in kilogram.

Entropy and temperature of the black hole

The entropy S of a black hole of surface has is given by:

$S\; =\; \backslash \; frac\; \{Akc^3\}\; \{4\; \{\backslash \; hbar\}\; G\}$

and its temperature T by:

$T\; =\; \backslash \; frac\; \{8\; \{\backslash \; pi\}\; kGM\}$

Life time of a black hole

The life time of a black hole before complete evaporation is given by:

$t\_V\; =\; \backslash \; frac\; \{15360\; \backslash \; pi\; \{G^2M^3\}\}\; \{\backslash \; hbar\; \{c^4\}\}$

Luminosity of a black hole

The Luminosity, expressed in Watt, of a black hole is given by:

$L\; =\; \backslash \; frac\; \{\backslash \; hbar\; \{c^6\}\}\; \{15360\; \backslash \; pi\; \{G^2M^2\}\}$

Energy and frequency of the radiation of Hawking

The energy, expressed in Joule of the radiation of Hawking emitted by a black hole is:

$E\; =\; \backslash \; frac\; \{\backslash \; hbar\; \{c^3\}\}\; \{8\; \{G\; \{M\}\}\}$

The Frequency, in Hertz, of the radiation of Hawking emitted by a black hole is:

$f\; =\; \backslash \; frac\; \{c^3\}\; \{16\; \backslash \; pi\; \{G\; \{M\}\}\}$

External bonds

Derivation of the formulas