phenomenon

gravitational wave propagation

Transmission of ripples in spacetime through gravitational interactions and media.
20 related articles · 6 formulas

Description

Gravitational wave propagation is the process by which ripples in spacetime travel outward from violent cosmic events, such as black hole mergers or supernovae. These waves are disturbances in the geometry of spacetime itself, predicted by Einstein's general relativity, and they carry information about their origins across the universe. Unlike electromagnetic waves, gravitational waves pass through matter almost undisturbed, making them unique messengers that can reveal details about events that light cannot reach.

History

First predicted by Albert Einstein in 1916 as a consequence of general relativity, they were indirectly confirmed by observations of the Hulse-Taylor binary pulsar in the 1970s, and directly detected by LIGO in 2015.

How it works

Gravitational waves are generated when massive objects accelerate asymmetrically, causing quadrupole moments to change. The waves propagate at the speed of light, stretching and squeezing spacetime in a transverse pattern perpendicular to their direction of travel. As they travel, they interact weakly with matter, which is why they can cross the universe without significant absorption or scattering, preserving the original signal's characteristics.

In practice

Gravitational wave detectors like LIGO and Virgo use laser interferometry to measure tiny distortions in spacetime, enabling the study of black holes, neutron stars, and the early universe.

Fun fact

Gravitational waves lose energy as they propagate, but the total energy emitted in a single black hole merger can exceed the combined light output of all stars in the observable universe for a brief moment.

Concept graph →

Formulas

$$h_{ij}^{\text{TT}} = \frac{2G}{c^4 D} \frac{d^2 I_{ij}}{dt^2}$$
Gravitational wave strain from mass quadrupole moment.
What is in the formula
h_{ij}^{\text{TT}}variableTransverse-traceless gravitational wave strain tensor — gravitational wave strain
DvariableDistance from source to observer — distance metre
I_{ij}variableMass quadrupole moment tensor — mass quadrupole moment kilogram metre squared
tvariableTime — time second
GconstantConstant of gravitation in Newton's law — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared
cconstantUniversal speed limit and speed of light in vacuum — speed of light = 299792458 metre per second
d^2/dt^2operatorSecond derivative with respect to time — second time derivative
h_{ij}^{{tt}}=\frac{2g}{c^4d}\frac{d^2i_{ij}}{dt^2} · 2605.01216v1
h_{ij}^{tt}=\frac{2g}{c^4r}\ddot{q}_{ij}^{tt} · 2607.03904
$$\mathcal{R} = 2\Lambda + 16\pi G \rho + \Theta^i_j \Theta^j_i - \Theta^2$$
Relates spatial curvature to density and velocity gradients.
What is in the formula
\mathcal{R}variableRicci scalar — ricci scalar per metre squared
\LambdavariableCosmological constant — cosmological constant per metre squared
\rhovariableMass density — mass density kilogram per cubic metre
\Theta^i_jvariableExpansion tensor — expansion tensor per second
\ThetavariableExpansion scalar — expansion scalar per second
GconstantNewton's constant of gravitation — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared
\mathcal{r}=2\lambda+16πg\varrho+\theta^i_j\theta^j_i-\theta^2 · 2605.05454v1
$$\dot{f}_{\mathrm{GW}} = \frac{96}{5} \pi^{8/3} \frac{G^{5/3}}{c^5} \mathcal{M}^{5/3} f_{\mathrm{GW}}^{11/3}$$
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
$$M = \frac{R v^2}{G}$$
Mass relates to radius and velocity dispersion.
What is in the formula
MvariableTotal mass of the system — mass kilogram
RvariableCharacteristic radius of the system — radius metre
vvariableVelocity dispersion (typical random velocity) — velocity dispersion metre per second
GconstantConstant of universal gravitation — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared
m<\frac{r_{phot}v_{blue,95\%}^2}{2g} · 2606.30711
$$\sin \theta = \frac{q}{r} \sqrt{ \frac{1 + 2GM/(q v_{\infty}^2)}{1 - 2GM/(r v_{\infty}^2)} }$$
Angle for gravitational scattering trajectories.
What is in the formula
thetavariabledeflection angle — angle radian
qvariabledistance of closest approach in absence of gravity — distance metre
rvariableradial distance from the gravitating body — distance metre
Mvariablemass of the gravitating body — mass kilogram
v_infinityvariablespeed of the test particle at infinity — velocity metre per second
GconstantUniversal constant of gravitation — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared
sinoperatortrigonometric sine function — sine
sqrtoperatortakes the square root of the argument — square root
\sinθ_c=\frac{q}{r}\sqrt{\frac{1+2gm_{\odot}/(qv_{\infty}^2)}{1-2gm_{\odot}/(rv_{\infty}^2)}} · 2607.04216v1
$$K = rac{2 π a • υ • ω}{P}$$
Relates orbital velocity amplitude to semi-major axis and period.
What is in the formula
Kvariableradial velocity semi-amplitude — velocity metre per second
avariablesemi-major axis — length metre
υvariableorbital velocity — velocity metre per second
ωvariableangular frequency — angular frequency radian per second
Pvariableorbital period — time second
k=\frac{2πa\sini}{p} · 2607.05193

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