effect

gravitational redshift

The shift in photon frequency due to gravitational potential differences, tested with atomic clocks and light.
10 related articles · 6 formulas

Description

Gravitational redshift is the phenomenon where light (or any electromagnetic radiation) loses energy as it climbs out of a gravitational well, shifting toward the red end of the spectrum. Conversely, light falling into a gravitational well gains energy and shifts toward the blue. This is a direct consequence of Einstein's general relativity: gravity affects the flow of time, and a photon's frequency is tied to the ticking of a clock at its location. The effect is tiny on Earth's surface but becomes significant near compact objects like neutron stars or black holes, and it is a key prediction that distinguishes general relativity from Newtonian gravity.

History

The concept was first predicted by Albert Einstein in 1907 and refined in his 1915 general theory of relativity. The first terrestrial measurement was made by Robert Pound and Glen Rebka in 1959 using gamma rays over a 22.5-meter tower at Harvard University.

How it works

In general relativity, a clock deeper in a gravitational potential runs slower than one higher up. A photon emitted from the lower clock has a frequency set by that slower ticking; when it reaches the higher observer, it is compared to their faster clock, so it appears to have a lower frequency — hence redshifted. The energy loss is not a frictional effect but a consequence of the geometry of spacetime: the photon's path through curved spacetime conserves energy in a way that depends on the gravitational potential difference between emission and reception.

In practice

Gravitational redshift is routinely accounted for in Global Positioning System (GPS) satellites, where clocks on orbit run faster than those on the ground by about 38 microseconds per day; corrections are applied to maintain positioning accuracy.

Fun fact

The effect is so precisely measured that atomic clocks on Earth's surface tick at different rates when separated by just one meter of altitude.

Concept graph →

Formulas

$$\dot{f}_{\mathrm{GW}} = \frac{96}{5} \pi^{8/3} \frac{G^{5/3}}{c^5} \mathcal{M}^{5/3} f_{\mathrm{GW}}^{11/3}$$
The rate of change of gravitational wave frequency depends on chirp mass.
What is in the formula
\dot{f}_{\mathrm{GW}variabletime derivative of gravitational wave frequency — frequency derivative hertz per second
\mathcal{M}variablechirp mass of the binary system — chirp mass kilogram
f_{\mathrm{GW}}variablegravitational wave frequency — frequency hertz
Gconstantconstant of universal gravitation — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared
cconstantspeed of light in vacuum — speed of light = 299792458 metre per second
\dot{f}_{{gw}}=\frac{96}{5}π^{8/3}\frac{g^{5/3}}{c^5}μm^{2/3}f_{{gw}}^{11/3} · 2605.10976v1
\dot{f}_0=\frac{96}{5}π^{8/3}(\frac{gm_c}{c^3})^{5/3}f_0^{11/3} · 2606.29039
$$ackslash Omega_* = ackslash sqrt{ rac{G M_*}{R_*^3}}$$
Angular frequency where centrifugal force equals gravity.
What is in the formula
Ω_*variablebreakup angular frequency — angular frequency radian per second
M_*variablemass of the rotating body — mass kilogram
R_*variableradius of the rotating body — radius metre
GconstantUniversal constant of gravitation — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared
ω_*=\sqrt{\frac{gm_*}{r_*^3}} · 2606.02692v1
$$\nu \propto m_a$$
Axion-photon conversion frequency is proportional to axion mass.
What is in the formula
νvariableFrequency of the converted photon — frequency hertz
m_avariableAxion mass — mass kilogram
∝operatorIndicates that the left side scales linearly with the right side — proportionality
ν\simeq242{мгц}(\frac{m_a}{μ{эв}}) · 2606.04304v1
$$1 + z = \sqrt{\frac{1 + \beta}{1 - \beta}}$$
Relativistic formula for redshift due to relative motion.
What is in the formula
zvariableRedshift parameter — redshift
βvariableRelative velocity divided by speed of light — velocity ratio
$$1+z_a=\sqrt{\frac{1+β}{1-β}},\quadβ=v/c$$ · 2606.05312v1
$$\frac{\Delta f}{f} = \frac{g \Delta h}{c^2}$$
Clock frequency increases with height in a gravitational field.
What is in the formula
ΔfvariableChange in clock frequency — frequency change hertz
fvariableClock frequency at reference height — frequency hertz
gvariableLocal gravitational acceleration — gravitational acceleration metre per second squared
ΔhvariableHeight difference — height difference metre
cconstantSpeed of light in vacuum — speed of light = 299792458 metre per second
\frac{δf}{f}=\frac{gδh}{c^2} · 2604.17157
$$f_{\rm reh} \propto T_{\rm reh}$$
Gravitational wave knee frequency scales with reheating temperature.
What is in the formula
f_rehvariableGravitational wave knee frequency at reheating — frequency hertz
T_rehvariableReheating temperature — temperature kelvin
f_{\rmreh}\simeq3.8*10^{-8}(\frac{t_{\rmreh}}{\rmgev}){\rmhz} · 2605.00735v1

Related articles · 10

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