Linearised Gravity and Gravitational Waves
Small departures from flat spacetime obey a wave equation, so a changing mass distribution sends ripples of geometry that stretch one transverse direction while squeezing the other. Detectors measure that strain, and it is tiny because geometry couples weakly to matter.
What a learner can do afterwards
- Explains why the linearised equations resemble electromagnetic radiation with a different source
- Describes what a passing wave does to a ring of freely floating test masses
- Says why there is no monopole or dipole gravitational radiation
1 · Read
Mass and energy warp the spacetime around them, and objects follow the straightest paths through that warped geometry. Small departures from flatness obey a wave equation, so accelerating lumps send ripples outward at the speed of light. The derivation reads against electromagnetic radiation, with a different source doing the shaking.
Not every motion radiates. A smooth steady change stays silent, while lumpy unsymmetric acceleration sings: two black holes or neutron stars spiraling together, or a massive star collapsing. Steady currents broadcast nothing, and the same holds for gravity.
A passing wave never pushes you forward; it stretches one sideways direction while squeezing the other, then swaps, over and over. A ring of freely floating marbles becomes an oval, first tall and thin, then wide and flat. Even balanced pulsing and wobbling stay silent as monopole and dipole: only uneven quadrupole lumps qualify.
The effect is tiny because geometry couples to matter very weakly. Even waves from colliding black holes shift a several kilometer detector arm by far less than a proton width. LIGO bounces laser light between mirrors to measure that strain, and in 2015 it caught merging black holes, opening listening alongside looking.
Moving lumps shake spacetime at light speed, squeeze rings sideways, and whisper so faintly that lasers must strain to hear.
2 · Watch
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8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.