quantity

gravitational wave strain

gravitational wave strain — from formula anatomy
14 related articles · 3 formulas

Description

Gravitational wave strain is a dimensionless measure of how much a passing gravitational wave stretches and squeezes spacetime. It is defined as the fractional change in distance between two free-falling test masses: if the original separation is L and the wave changes it by ΔL, the strain is h = ΔL / L. Because spacetime itself is being distorted, the strain is not a force pushing objects apart; rather, it is a geometric effect that alters the very metric of space.

History

The concept of gravitational wave strain was formalized in the early 20th century through Einstein's general relativity, with the first explicit derivation of gravitational waves by Einstein in 1916. The first direct detection of strain was made by the LIGO collaboration in 2015.

How it works

A gravitational wave is a ripple in the curvature of spacetime, produced by accelerating massive objects (like merging black holes or neutron stars). As the wave passes, it alternately stretches space along one axis while compressing it along a perpendicular axis. The strain quantifies the amplitude of this distortion. For a wave traveling along the z-axis, the two polarizations (plus and cross) cause the separation between test masses to oscillate with a characteristic pattern. The strain is typically extremely small — for events detected by LIGO, h is on the order of 10^-21, meaning a change of one part in a billion trillion.

In practice

Gravitational wave detectors like LIGO and Virgo measure strain directly using laser interferometry, where the tiny changes in arm lengths (on the order of 10^-18 meters) are detected as phase shifts in the laser light.

Fun fact

The strain from the first detected gravitational wave (GW150914) was smaller than the diameter of a proton, yet it carried information about the merger of two black holes 1.3 billion light-years away.

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
$$\tilde{h}_L(f) = \sum_j |\mu_j|^{1/2} e^{2\pi i f \Delta t_j - i\pi n_j} \tilde{h}_{\rm src}(f)$$
Lensed gravitational wave signal sum over images.
What is in the formula
h̃_LvariableLensed gravitational wave signal in frequency domain — gravitational wave strain
fvariableGravitational wave frequency — frequency hertz
μ_jvariableMagnification factor of image j — magnification
Δt_jvariableTime delay of image j relative to source — time delay second
n_jvariableMorse index of image j — morse index
h̃_srcvariableUnlensed source gravitational wave signal — gravitational wave strain
∑operatorSum over lensed images — summation
e^{...}operatorComplex exponential encoding phase shifts — exponential
$$h_L(f) = \mu(f) h_{unL}(f)$$
Lensed wave equals unlensed wave multiplied by magnification factor.
What is in the formula
h_LvariableLensed gravitational wave strain — gravitational wave strain
h_unLvariableUnlensed gravitational wave strain — gravitational wave strain
μvariableMagnification factor — magnification

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