Primordial Black-Hole and Macroscopic Dark-Matter Constraints with LISA

The detectability of gravitational waves originating from primordial black holes or other large macroscopic dark-matter candidates inspiraling into Sagittarius ${\rm A}^{\!*}$ is investigated. It is shown that LISA should be a formidable machine to detect the stochastic signal from the accumulated collection of such objects that have been gravitationally captured by Sgr$\,{\rm A}^{\!*}$, provided they have masses above $\sim 10^{-20}\,M_{\odot}$. This is especially so, if they are the main component of the dark matter, and the dark-matter density at Sagittarius ${\rm A}^{\!*}$ exceeds its value in the solar-neighborhood. Notably, the window of mass that is unconstrained by various gravitational lensing arguments and observations, $2 \times 10^{20}\,{\rm g} \leq m_{\rm DM} \leq 4 \times 10^{24}\,{\rm g}$, will be accessible. Forecasts are derived for the event rates and signal strengths as a function of dark-matter mass, assuming that the dark-matter candidates are not tidally disrupted during the inspiral. This is certainly the case for primordial black holes, and it shown that it is also very likely the case for candidate objects of nuclear density.