Einstein Luminosity and Speed of Light

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The discussion focuses on calculating the Einstein luminosity (LE) using dimensional analysis based on the speed of light (c) and the gravitational constant (G). The derived formula for luminosity is L = c^5/G, indicating that this value represents the maximum brightness an object can achieve before becoming a black hole. It is established that if an object's luminosity exceeds 0.5LE, it cannot radiate energy fast enough without collapsing into a black hole. Participants also discuss the implications of radiation escaping at the speed of light and the energy required for collapse. The conversation highlights the relationship between luminosity, energy, and black hole formation.
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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!
 
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Please do your 250 homework by yourself.
 
Black holes sound ominous...

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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?
 

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