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What are neutron stars made of? Gravitational waves may reveal the answer

Neutron stars are one of the most mysterious wonders in the Universe. Their extreme densities hint at new and exotic physics at work within. Gravitational waves could be the key to unlocking their secrets. In particular, a first detection of gravitational waves from rapidly-spinning, deformed neutron stars could yield new insights into the physics of matter at extreme densities and under strong gravity. Once a first detection is made, a critical challenge will be to robustly extract physically interesting information from the detected signals. In this essay, we describe initial research towards answering this challenge, and thereby unleashing the full power of gravitational waves as an engine for the discovery of new physics.