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Black Hole Event Horizon Area with Charge

An event horizon is a boundary in spacetime beyond which events cannot affect an outside observer.

The event horizon area increases roughly quadratically with the mass and charge.

Formula

QuantityVariable["A", "Area"] == 4*Pi*(Quantity[1, "GravitationalConstant"/"SpeedOfLight"^2]*QuantityVariable["M", "Mass"] + Sqrt[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
A event horizon area "Area"
M mass "Mass"
Q electric charge "ElectricCharge"

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Black Hole Event Horizon Area with Charge"]
Out[1]=

Get the formula:

In[2]:=
FormulaData[ ResourceObject["Black Hole Event Horizon Area with Charge"]]
Out[2]=

Use some values:

In[3]:=
FormulaData[ ResourceObject[ "Black Hole Event Horizon Area with Charge"], {QuantityVariable[ "A","Area"] -> Quantity[1.`*^11, ("Meters")^2]}]
Out[3]=

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