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Black Hole Entropy

The entropy of a black hole is derived from its effective temperature. The temperature of a black hole is calculated as if the electromagnetic radiation it emits came from a blackbody.

The entropy of a black hole increases quadratically with increasing mass and angular momentum. It increases linearly with increasing charge.

Formula

QuantityVariable["S", "Entropy"] == Quantity[Pi, ("BoltzmannConstant"*"SpeedOfLight"^3)/("GravitationalConstant"*"ReducedPlanckConstant")]*((Quantity[1, "SpeedOfLight"^(-2)]*QuantityVariable["J", "AngularMomentum"]^2)/QuantityVariable["M", "Mass"]^2 + (Quantity[1, "GravitationalConstant"/"SpeedOfLight"^2]*QuantityVariable["M", "Mass"] + Sqrt[(Quantity[-1, "SpeedOfLight"^(-2)]*QuantityVariable["J", "AngularMomentum"]^2)/QuantityVariable["M", "Mass"]^2 + Quantity[1, "GravitationalConstant"^2/"SpeedOfLight"^4]*QuantityVariable["M", "Mass"]^2 + Quantity[-1/(4*Pi), "GravitationalConstant"/("ElectricConstant"*"SpeedOfLight"^4)]*QuantityVariable["Q", "ElectricCharge"]^2])^2)

symbol description physical quantity
S entropy "Entropy"
J angular momentum "AngularMomentum"
M mass "Mass"
Q electric charge "ElectricCharge"

Forms

Examples

Get the resource:

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

Get the formula:

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

Use some values:

In[3]:=
FormulaData[ ResourceObject[ "Black Hole Entropy"], {QuantityVariable["Q","ElectricCharge"] -> Quantity[-10.`, "Coulombs"], QuantityVariable["J","AngularMomentum"] -> Quantity[-10.`, "Joules" "Seconds"]}]
Out[3]=

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