MadSci Network: Astronomy
Query:

Re: Do all black holes have the same gravity at the event horizon?

Date: Wed Sep 3 21:01:24 2003
Posted By: Irene Little, Faculty, CASA, University of Colorado
Area of science: Astronomy
ID: 1061248590.As
Message:

Is the gravity at the event horizons of different black holes exactly the same 
in strength?

That is a very interesting question and I had to think about it.  It turns
out that the Force of  Gravity at the event horizon is inversely
proportional to the mass of the Black Hole.  That means that the more
massive the Black Hole, the weaker the force of gravity is at the event
horizon.  The reason for that is that the radius of the event horizon depends
directly on the mass of the Black Hole and the Force of Gravity depends
inversely on the square of the event horizon radius.  The radius of the event
horizon is called the Schwarzschild radius.

[Mod note: in what follows, "^" means superscript, ie c^2 is c-squared.]

Force of Gravity (at the event horizon)= [G* (mass at the event
horizon)*(mass of the Black Hole)] divided by (Radius Schwarzschild)^2

Radius_Schwarzschild = [2 G *(mass Black Hole)] divided by c^2

Substituting for R_Schwarzschild in F(event horizon)

F(event horizon) = [G * (mass at event horizon) *(mass Black hole) (c^2)^2] /
  [4 G^2 *(mass Black hole)^2]

Simplifying the equations gives:

F(event horizon) = [1/4 * mass(at event horizon) * c^4] /[ G*(mass Black Hole)]

Where G is the universal gravitational constant and c is the speed of light.





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