Does the Gravitational Force at the Event Horizon Increase with Black Hole Mass?

AI Thread Summary
The discussion focuses on the behavior of gravitational force at the event horizon of a black hole as its mass increases. It is suggested that the gravitational force remains constant at the event horizon because the Schwarzschild radius increases proportionally with mass. The participant is encouraged to compare the Schwarzschild radius with the Newtonian gravitational acceleration formula, g = GM/r², for qualitative insights. There is a call for deriving an expression for gravitational acceleration specifically at the Schwarzschild radius. The conversation emphasizes understanding the relationship between mass, radius, and gravitational force in the context of black holes.
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Homework Statement


I got a problem wrong on a quiz and I'm pretty positive on all the other questions as being correct but maybe this one..

How does the gravitational force at the event horizon (Schwarzschild radius) behave as the black hole mass increases?


Homework Equations





The Attempt at a Solution



I assumed that by definition of the event horizon the force is constant no matter how the mass changes since the radius will move with it. Is this correct?
 
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Start with the expression for the Schwarzschild radius. Compare with the expression for gravitational acceleration (I think the Newtonian version g = GM/r2 will do for qualitative results). Can you create an expression gravitational acceleration at the Schwarzschild radius?
 

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