concept

gravitational waves

Gravitational waves are ripples in spacetime that propagate as waves and are generated by accelerating masses.
51 related articles · 5 formulas · 6 who worked here

Description

Gravitational waves are oscillations of the geometry of spacetime, propagating at the speed of light. They are generated by accelerated motions of massive bodies with broken spherical symmetry: binary systems, supernova explosions. The wave has a quadrupole nature: it alternately compresses and stretches distances in perpendicular directions, corresponding to two polarizations — 'plus' and 'cross'. At the moment of black hole merger, the radiation can briefly surpass in power the combined luminosity of all stars in the observable Universe.

History

The idea of gravitational waves was first proposed by Henri Poincaré (1905), but the rigorous prediction was made by Albert Einstein (1916, 1918) based on the linearized equations of GR. For a long time, the existence of waves was disputed, even by Einstein himself. Experimental searches began with the pioneer detectors of Joseph Weber in the 1960s. Only in 2015 did the LIGO collaboration (founders Rainer Weiss, Kip Thorne) detect the direct merger of black holes.

How it works

From Einstein's equations G_μν = (8πG/c⁴) T_μν, by linearization one obtains the wave equation for perturbations □h_μν = 0 in vacuum. An interferometric detector (LIGO, Virgo) measures the path difference of beams in the arms caused by the change in distance under the wave's influence: for h ~ 10⁻²¹, the displacement is 10⁻¹⁸ m for a 4 km arm.

In practice

Detectors like LIGO pick up these oscillations, revealing previously invisible mergers of black holes and neutron stars, and in the future — gravitational-wave astronomy for studying the dark eras of the cosmos.

Fun fact

The signal of the first detection (GW150914) lasted only 0.2 seconds, but during that time three solar masses were converted into gravitational waves — equivalent to billions of billions of atomic bombs.

Concept graph →

Formulas

$$h_0 = \frac{4\pi^2 G}{c^4} \frac{\varepsilon I_{zz} f_{\rm GW}^2}{d}$$
The amplitude of gravitational waves from a rotating ellipsoid.
What is in the formula
h_0variablegravitational wave strain amplitude — strain
εvariableellipticity — ellipticity
I_zzvariablemoment of inertia about rotation axis — moment of inertia kilogram metre squared
f_GWvariablegravitational wave frequency — frequency hertz
dvariabledistance to source — distance metre
GconstantNewton's constant 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
h_0=\frac{4π^2g}{c^4}\frac{\varepsiloni_{zz}f_{\rmgw}^2}{d} · 2606.05082v1
$$h = \frac{4 G^{5/3} \mathcal{M}^{5/3} (\pi f)^{2/3}}{c^4 d}$$
Amplitude depends on chirp mass, frequency, and distance.
What is in the formula
hvariablegravitational wave strain amplitude — gravitational wave amplitude
Mvariablechirp mass of the binary system — chirp mass kilogram
fvariablegravitational wave frequency — frequency hertz
dvariableluminosity distance to the source — distance metre
GconstantNewtonian constant of 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
a=\frac{2(gm_c)^{5/3}}{c^4d_l}(πf_0)^{2/3} · 2606.29039
$$\frac{D^2 \xi^\mu}{d\tau^2} = -R^\mu{}_{\nu\rho\sigma} u^\nu u^\rho \xi^\sigma$$
Gravitational waves cause relative acceleration between test masses.
What is in the formula
ξ^μvariabledeviation vector between two nearby geodesics — geodesic deviation vector metre
τvariableproper time along the geodesic — proper time second
u^νvariablefour-velocity of the geodesic — four velocity
u^ρvariablefour-velocity of the geodesic (repeated index) — four velocity
ξ^σvariabledeviation vector (repeated index) — geodesic deviation vector metre
D^2/dτ^2operatorsecond covariant derivative along the geodesic — covariant second derivative
δ\ddot{r}_i=\frac{1}{2}\ddot{h}_{ij}^{tt}r_j · 2607.18390v1
$$v^2 = \frac{G M}{r}$$
Orbital speed squared equals gravitational constant times mass over radius.
What is in the formula
vvariableorbital speed — velocity metre per second
Mvariablecentral mass — mass kilogram
rvariableorbital radius — radius metre
GconstantUniversal constant of gravitation, determining the strength of gravitational force. — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared
v^2(r)=\frac{gm(<r)}{r} · 2604.06917
$$\frac{\Delta f}{f} = \frac{g \Delta h}{c^2}$$
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

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