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Black Hole Lifetime

A black hole will eventually disappear (or evaporate) due to escaping Hawking radiation. The lifetime of a nonrotating, noncharged Schwarzschild black hole can be derived from the formulas for the Schwarzschild radius of the black hole, the Stefan–Boltzmann law of blackbody radiation, the temperature of the Hawking radiation and the formula for the surface area of a sphere.

The lifetime of a black hole increases cubically with increasing initial mass.

Formula

QuantityVariable["t", "Age"] == Quantity[5120*Pi, "GravitationalConstant"^2/("ReducedPlanckConstant"*"SpeedOfLight"^4)]*QuantityVariable["M", "Mass"]^3

symbol description physical quantity
t lifetime "Age"
M mass "Mass"

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Black Hole Lifetime"]
Out[1]=

Get the formula:

In[2]:=
FormulaData[ResourceObject["Black Hole Lifetime"]]
Out[2]=

Use some values:

In[3]:=
FormulaData[ ResourceObject[ "Black Hole Lifetime"], {QuantityVariable["t","Age"] -> Quantity[1.`*^50, "Years"]}]
Out[3]=

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