Source: http://archive.ncsa.illinois.edu/Cyberia/NumRel/GravWaves.html
What are gravity waves?
Disturbances in the curvature of space time caused by the motions of matter.
How do we try detect them?
Although these waves are really tough to track, the idea is that if something is giving off gravity waves then it has to be decreasing in mass.
Why are gravity waves important?
Unlike electromagnetic waves gravity waves don't change through space. They travel through everything unharmed, which means they could help alter the way the universe is currently mapped out.
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