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

In summary, the question asks about the behavior of the gravitational force at the event horizon as the black hole mass increases. The student assumed that the force would remain constant due to the definition of the event horizon and the corresponding change in radius. The solution suggests comparing the Schwarzschild radius expression with the expression for gravitational acceleration, and creating an expression for gravitational acceleration at the event horizon.
  • #1
bowlbase
146
2

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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  • #2
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?
 

1. What is the event horizon in relation to gravity?

The event horizon is a theoretical boundary around a black hole where the escape velocity is equal to the speed of light. This means that any object, including light, cannot escape from within the event horizon.

2. How does the gravity of the event horizon affect objects outside of it?

The gravity of the event horizon is extremely strong and can affect objects outside of it by warping space and time. This can cause objects to orbit or be pulled towards the black hole.

3. Can the gravity of the event horizon be measured?

Yes, the gravity of the event horizon can be measured indirectly by observing the effects it has on surrounding objects, such as their orbits or the bending of light. It can also be measured using mathematical equations.

4. Is there a limit to the strength of the gravity at the event horizon?

According to Einstein's theory of general relativity, there is no limit to the strength of gravity at the event horizon. However, at the center of a black hole, the gravity becomes infinitely strong, resulting in a singularity.

5. How does the gravity of the event horizon impact time?

The gravity of the event horizon slows down time, known as gravitational time dilation. This means that time moves slower for objects near the event horizon compared to those further away. This phenomenon has been observed and confirmed by scientists.

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