Deriving Formula for Surface Area of Black Hole

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In summary, the conversation discusses Einstein's theory of general relativity, which involves the speed of light and Newton's constant. The task is to use dimensional analysis to derive a formula for the surface area of a black hole based on its mass, with a dimensionless proportionality constant. The participants of the conversation express their difficulty in solving the problem and eventually figure out the solution.
  • #1
Werg22
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Homework Statement



Einstein's theory of general relativity is relativistic model of gravity. "Relativistic" means it involves the speed of light, c; "gravity" means it involves Newton's constant, G. Use dimensional analysis to derive a formula for the surface area, A, of a black hole of mass M, up to a dimensionless proportionality constant.

Homework Equations



N/A

The Attempt at a Solution



I have little idea of how to tackle this question. Any sort of help would be appreciable.
 
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  • #2
Can anyone be of help?
 
  • #3
Bumping up again.
 
  • #4
werg lol phys 121 assignment 1 question 3 lol... hahaha waterloo university right?
 
  • #5
I couldn't do the last Problem... What did u get for (a) and (b)
 
  • #6
As far as I can tell, the idea is to propose something along the lines of:

A= k*c^x*G^y*M^z

Where k is a dimensionless constant.

Then figure out what the exponents x,y and z must be so that the right hand has units of area (length^2). You should come up with a system of equations with only one solution.
 
  • #7
I ended by figuring it out, thanks Proggle anyway. The question is kind of obscure and the solution isn't very intuitive.

Yes Karma I go to the University of Waterloo, I figured the same with you by your car race question.
 

Related to Deriving Formula for Surface Area of Black Hole

1. What is the formula for calculating the surface area of a black hole?

The formula for calculating the surface area of a black hole is A = 4πr2, where A is the surface area and r is the radius of the black hole.

2. How is the surface area of a black hole different from its event horizon?

The surface area of a black hole refers to the area of the event horizon, which is the boundary surrounding the black hole from which nothing can escape, not even light. The event horizon is the point of no return for anything that enters the black hole.

3. How is the surface area of a black hole related to its mass?

The surface area of a black hole is directly proportional to its mass. This means that as the mass of the black hole increases, so does its surface area. This relationship is known as the area theorem, which states that the surface area of a black hole must always increase over time.

4. Can the surface area of a black hole change over time?

Yes, the surface area of a black hole can change over time. As matter falls into a black hole, its mass and therefore its surface area will increase. However, due to Hawking radiation, black holes can also lose mass and therefore decrease in surface area over time.

5. How is the surface area of a black hole related to its entropy?

The surface area of a black hole is directly proportional to its entropy. This is known as the Bekenstein-Hawking formula, which states that the entropy of a black hole is equal to one quarter of its surface area measured in Planck units.

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