# Gravitational redshift

 related topics {math, energy, light} {rate, high, increase}

In physics, light or other forms of electromagnetic radiation of a certain wavelength originating from a source placed in a region of stronger gravitational field (and which could be said to have climbed "uphill" out of a gravity well) will be found to be of longer wavelength when received by an observer in a region of weaker gravitational field. If applied to optical wave-lengths this manifests itself as a change in the colour of the light as the wavelength is shifted toward the red (making it less energetic, longer in wavelength, and lower in frequency) part of the spectrum.

This effect is called gravitational redshift and other spectral lines found in the light will also be shifted towards the longer wavelength, or "red," end of the spectrum. This shift can be observed along the entire electromagnetic spectrum. Light that has passed "downhill" into a region of stronger gravity shows a corresponding increase in energy, and is said to be gravitationally blueshifted.

## Contents

### Definition

Redshift is often denoted with the dimensionless variable $z\,$, defined as the fractional change of the wavelength[1]

$z=\frac{\lambda_o-\lambda_e}{\lambda_e}$

Where $\lambda_o\,$ is the wavelength of the electromagnetic radiation (photon) as measured by the observer. $\lambda_e\,$ is the wavelength of the electromagnetic radiation (photon) when measured at the source of emission.

The gravitational redshift can be calculated in the framework of General Relativity as

$z=\frac{1}{\sqrt{1-\frac{r_s}{r}}}-1$

with the Schwarzschild radius $r_s=\frac{2GM}{c^2}$, where G denotes Newton's gravitational constant, M the mass of the gravitating body, c the speed of light, and r the distance from the center of mass of the gravitating body.