Einstein Luminosity and Speed of Light

• kornha
In summary, the conversation discusses finding the Einstein luminosity in terms of c and G and determining a power using dimensional analysis. It is also mentioned that an object converting its mass to energy cannot radiate that energy away fast enough before becoming a black hole if its luminosity is greater than 0.5LE. Finally, it is stated that L = c^5/G and the conversation moves on to discussing the concept of black holes.
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!

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?

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.

1. What is Einstein's theory of relativity?

Einstein's theory of relativity is a scientific theory that explains the relationship between space and time. It has two components: special relativity, which deals with objects moving at a constant speed, and general relativity, which accounts for gravity and the curvature of space-time.

2. What is Einstein's equation, E=mc^2, and what does it mean?

E=mc^2 is Einstein's famous equation, where E represents energy, m represents mass, and c represents the speed of light. This equation shows that mass and energy are equivalent and can be converted into each other. It also states that the speed of light is the maximum speed at which energy and mass can be exchanged.

3. How did Einstein's theory of relativity impact our understanding of the universe?

Einstein's theory of relativity revolutionized our understanding of the universe by providing a new way to think about space and time. It showed that the laws of physics are the same for all observers, regardless of their relative motion, and that the speed of light is a fundamental constant. It also explained the behavior of objects at high speeds, such as in the theory of black holes.

4. What is Einstein's luminosity formula and how is it related to the speed of light?

Einstein's luminosity formula is a mathematical expression that relates an object's luminosity (a measure of its brightness) to its mass and the speed of light. It states that the more massive an object is, the more energy it can release as light. This formula is derived from the equation E=mc^2, showing the close relationship between mass, energy, and the speed of light.

5. Is the speed of light truly constant or can it be exceeded?

According to Einstein's theory of relativity, the speed of light is the maximum speed at which all matter and information can travel. This has been confirmed through numerous experiments and observations. While there are some theories that suggest the existence of particles that can travel faster than light, there is no solid evidence to support this claim at this time.

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