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Black Hole Temperature

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

The temperature at the horizon of a black hole decreases with increasing mass or charge, and increases with increasing angular momentum.

Formula

QuantityVariable["T", "Temperature"] == (Quantity[1/(2*Pi), ("ReducedPlanckConstant"*"SpeedOfLight")/"BoltzmannConstant"]*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])/(Quantity[-1/(4*Pi), "GravitationalConstant"/("ElectricConstant"*"SpeedOfLight"^4)]*QuantityVariable["Q", "ElectricCharge"]^2 + Quantity[2, "GravitationalConstant"/"SpeedOfLight"^2]*QuantityVariable["M", "Mass"]*(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]))

Forms

Examples

Get the resource:

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

Get the formula:

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

Use some values:

In[3]:=
FormulaData[ ResourceObject[ "Black Hole Temperature"], {QuantityVariable["T","Temperature"] -> Quantity[1.`*^-9, "Kelvins"], QuantityVariable["Q","ElectricCharge"] -> Quantity[1.`*^-10, "Coulombs"]}]
Out[3]=

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