# Gravitational Redshift: Derivation from Static Metric

• I
• redtree
In summary, the conversation discusses possible methods for determining the time between two events where null geodesics cross a certain radius and how changes in proper time relate to changes in frequency as measured by redshift. One method involves computing the proper time along a worldline of constant radius, while another method involves computing the energy at infinity of a null geodesic. The conversation also explores the relationship between time and frequency as Fourier conjugates and whether a quantum perspective can be imposed on a non-quantum theory.
redtree
I am trying to find a derivation of gravitational redshift from a static metric that does not depend on the equivalence principle and is not a heuristic Newtonian derivation. Any suggestions?

Solve for a null geodesic. Start one at ##(r,t_1)## and the other at ##(r,t_1+\Delta t)##. Determine the time between the events where the two geodesics cross some radius ##R##?

Ibix said:
Determine the time

More precisely, the proper time along a worldline of constant radius ##R## (the radius of reception), as compared with the proper time along a worldline of constant radius ##r## (the radius of emission).

Another method would be to compute the energy at infinity of a null geodesic, and then show how that relates to its energy as measured by static observers at ##r## and ##R##.

Ibix
Given that time and frequency are Fourier conjugates, how can changes in proper time relate directly to changes in frequency (as measured by redshift)? Or am I imposing a quantum perspective on a non-quantum theory?

redtree said:
Given that time and frequency are Fourier conjugates, how can changes in proper time relate directly to changes in frequency (as measured by redshift)? Or am I imposing a quantum perspective on a non-quantum theory?
You are.

To get the time dilation, all you need is the proper time between emission of successive peaks at the source and the proper time between the arrival of these peaks at the destination. The ratio between the two is the time dilation factor. You could do this calculation with two flashes of light emitted an hour apart at the source if you wanted.

## 1. What is gravitational redshift?

Gravitational redshift is the phenomenon in which light appears to have longer wavelengths when observed from a region with a strong gravitational field, compared to when it is observed from a region with a weaker gravitational field.

## 2. What is the derivation of gravitational redshift?

The derivation of gravitational redshift involves using Einstein's general theory of relativity to calculate the change in frequency and wavelength of light as it travels through a strong gravitational field. This is achieved by solving the equations for the static metric, which describes the curvature of spacetime in the presence of a massive object.

## 3. Why is gravitational redshift important?

Gravitational redshift is important because it provides evidence for the effects of gravity on light, confirming the predictions of general relativity. It also has practical applications, such as in the precise measurement of time and in the functioning of GPS systems.

## 4. How does gravitational redshift differ from Doppler shift?

Gravitational redshift is the result of light traveling through a strong gravitational field, causing its wavelength to appear longer. Doppler shift, on the other hand, is the result of relative motion between the source of light and the observer, causing a shift in the wavelength of light due to the Doppler effect.

## 5. Can gravitational redshift be observed in everyday life?

Yes, gravitational redshift can be observed in everyday life. For example, the redshift of light from stars near the horizon of a black hole has been observed, as well as the slight redshift of light on Earth due to the Earth's gravitational field. However, these effects are very small and require precise measurements to be detected.

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