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Black Hole Surface Gravity

The surface gravity of a black hole with a static Killing horizon is the acceleration, as exerted at infinity, needed to keep an object at the horizon.

The surface gravity of a black hole decreases with increasing mass or charge, and increases with increasing angular momentum.

Formula

QuantityVariable["k", "GravitationalAcceleration"] == (Quantity[1, "SpeedOfLight"^2]*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]))

symbol description physical quantity
k surface gravity "GravitationalAcceleration"
J angular momentum "AngularMomentum"
M mass "Mass"
Q electric charge "ElectricCharge"

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Black Hole Surface Gravity"]
Out[1]=

Get the formula:

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

Use some values:

In[3]:=
FormulaData[ ResourceObject[ "Black Hole Surface Gravity"], {QuantityVariable[ "k","GravitationalAcceleration"] -> Quantity[1.`*^11, ("Meters")/("Seconds")^2], QuantityVariable["M","Mass"] -> Quantity[2.`*^30, "Kilograms"], QuantityVariable["J","AngularMomentum"] -> Quantity[1.`*^-19, "Joules" "Seconds"]}]
Out[3]=

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