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Primordial black holes of planetary masses captured by compact stars arewidely studied to constrain their composition fraction of dark matter. Such acapture may lead to an inspiral process and be detected through gravitationalwave signals. In this Letter, we study the post-capture inspiral process byconsidering two different kinds of compact stars, i.e., strange stars andneutron stars. The dynamical equations are numerically solved and thegravitational wave emission is calculated. It is found that the Advanced LIGOcan detect the inspiraling of a $10^{-5}$ solar mass primordial black hole at adistance of 10 kpc, while a Jovian-mass case can even be detected atmegaparsecs. Promisingly, the next generation gravitational wave detectors candetect the cases of $10^{-5}$ solar mass primordial black holes up to ${\sim}1$Mpc, and can detect Jovian-mass cases at several hundred megaparsecs. Moreover,the kilohertz gravitational wave signal shows significant differences forstrange stars and neutron stars, potentially making it a novel probe to thedense matter equation of state.

Gravitational-wave Emission from a Primordial Black Hole Inspiraling inside a Compact Star: a Novel Probe for Dense Matter Equation of State