Gravitation Redshift for very dense stars

In summary, the expression ##\frac{f'-f}{f}=\frac{gH}{c^2}=\frac{GM_s}{R_sc^2}## assumes that ##\triangle f## is small and that the photon has a constant mass. However, if a star is very dense, this assumption does not hold. To solve for ##f'##, we use the relationship ##f'=fe^{-GM_s/R_sc^2}## in part (a) and simplify to get ##f'=f(1-\frac{GM_s}{R_sc^2})## in part (b) for small ##M_s/R_s##.
  • #1
Rubber Ducky
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Homework Statement


In deriving the expression ##\frac{f'-f}{f}=\frac{gH}{c^2}=\frac{GM_s}{R_sc^2}## , it was assumed that ##\triangle f=f'-f## was small, and that the photon had a constant mass of ##\frac{hf}{c^2}##. Suppose that a star is so dense that ##\triangle f## is not small.

(a) Show that ##f'##, the photon frequency at ##\infty##, is related to ##f##, the photon frequency at the star's surface, by ##f'=fe^{-GM_s/R_sc^2}##

(b) Show that (a) reduces to ##f'=f(1-\frac{GM_s}{R_sc^2})## for small ##M_s/R_s##

Homework Equations


I believe all of the important ones were listed in the problem statement. I apologize if I missed some.

The Attempt at a Solution


I really have no idea where to start. The exponential in (a) seems to pop out of nowhere.
 
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  • #2
Thanks for the post! Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
 

1. What is Gravitational Redshift?

Gravitational Redshift is a phenomenon in which electromagnetic radiation, such as light, is shifted to longer wavelengths as it travels through a gravitational field. This can occur when the radiation is emitted from a dense object, such as a star, and travels through the intense gravitational pull of the object.

2. What causes Gravitational Redshift in stars?

Gravitational Redshift is caused by the intense gravitational force of a star. As light travels away from the star, it must overcome the pull of the star's gravity. This results in a decrease in the energy of the light, causing it to shift to longer wavelengths.

3. How does the density of a star affect Gravitational Redshift?

The denser a star is, the stronger its gravitational field. This means that if a star is very dense, the gravitational redshift will be more pronounced. The more massive and compact a star is, the more intense its gravitational field will be, resulting in a larger shift in the wavelength of light.

4. Can Gravitational Redshift be observed in our own Sun?

Yes, Gravitational Redshift has been observed in our Sun. However, the effect is very small, as the Sun is not as dense as other stars. It was first observed by Sir Arthur Eddington during a solar eclipse in 1919, when he noticed that the wavelengths of light from distant stars were shifted slightly as they passed near the Sun's gravitational field.

5. How does Gravitational Redshift impact our understanding of the universe?

Gravitational Redshift is an important phenomenon in our understanding of the universe. It provides evidence for the theory of General Relativity, which explains the relationship between gravity and the curvature of space-time. It also allows us to study the properties of very dense objects, such as neutron stars and black holes, which are some of the most extreme objects in the universe.

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