Einstein Luminosity and Speed of Light

[kornha]

Homework Statement

Find the Einstein luminosity (LE) in terms of just c and G (the speed of light
and the gravitational constant), i.e. determine a power (in watts) from just these two terms
using dimensional analysis. What is this value? Once determined, you should be able to
show that an object converting its mass entirely to energy cannot radiate that energy away
fast enough before becoming a black hole if its luminosity is greater than 0:5LE. Thus LE
represents an upper limit on how bright anything in our universe can be!

Homework Equations

There are no particular relevant equations. It helps to know that G is n m^3/(kg s^2) units and that c is m/s. Luminosity also equals Power.

The Attempt at a Solution

I solved the beginning. I found that the units of power are J/s which end up being (kg ms^2)/(s^3) and thus solving for a c and G combination yields that L = c^5/G.
However, I am completely unsure how to procede in the question passed the "Once determined you should be able to show..."
Please, any help would be great!

 

[Gladney]

Please do your 250 homework by yourself.

 

[YogaInstructor]

Black holes sound ominous...

I recommend you enroll in Yoga Instructor's restorative yoga class to relax the body...and mind. 15% discount for physics majors!

 

[clamtrox]

Hmm, what odd responses you got... So anyway, consider radiation moving away from the source at the speed of light. How much energy is contained in a sphere of radius ct and how much is needed to collapse it into a black hole?

 

[paranormal]

The next step is to use the equation L = c^5/G to find the value for the Einstein luminosity. The value will depend on the specific numerical values for c and G that are used, but it should be a very large number since c is a very large number and G is a very small number.

Once you have the value for the Einstein luminosity, you can use it to show that an object converting its mass entirely to energy cannot radiate that energy away fast enough before becoming a black hole if its luminosity is greater than 0.5LE. This means that the luminosity of the object must be less than or equal to 0.5 times the Einstein luminosity.

This is an important concept in astrophysics, known as the Eddington limit. It is the maximum luminosity that an object can have before the radiation pressure from the energy being released becomes so strong that it can overcome the gravitational force and cause the object to collapse into a black hole.

So, by understanding the relationship between the Einstein luminosity and the Eddington limit, we can see that the Einstein luminosity represents an upper limit on how bright anything in our universe can be. This is because if an object has a luminosity greater than the Einstein luminosity, it will eventually collapse into a black hole.

I hope this helps to clarify the question and how to approach it. Let me know if you have any further questions.