MadSci Network: Astronomy |
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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