Born in the Dark: The Catastrophic Collapse of Fuzzy Dark Matter Solitons as the Origin of Little Red Dots

JWST surveys have uncovered a population of compact, red sources ("Little Red Dots," LRDs) at $z \ge 5$ that exhibit broad Balmer emission yet remain X-ray faint, implying heavy obscuration with $N_H \ge 10^{24}$ cm$^{-2}$. We propose that LRDs may trace a short-lived, obscured phase associated with rapid baryonic inflow inside the deep solitonic cores of fuzzy dark matter (FDM) halos. Combining the soliton size scaling with (i) the observed compact radii ($r_e \sim 30-100$ pc) and (ii) the requirement that Compton-thick columns be achievable within a region of order the core radius, we find that particle masses $m$ few $\times 10^{-22}$ eV are plausible for soliton masses $M_s \sim 10^8 - 10^9 M_\odot$; we adopt $m_{22}=2$ as a fiducial choice. A conservative mass-budget estimate for the obscuring column, together with isothermal hydrostatic stratification, indicates that configurations reaching $N_H \ge 10^{24} - 10^{25}$ cm$^{-2}$ require densities for which radiative losses (cooling and/or diffusion) occur faster than the dynamical time, suggesting that a long-lived static hot atmosphere is unlikely (an "Opacity Crisis") and that rapid inflow or radiation-pressure-driven evolution is favored. Using $512^3$ pseudo-spectral Schr\"odinger-Poisson simulations of idealized soliton mergers, we illustrate that compact, high-density soliton cores can form via violent relaxation under representative scalings. We discuss observational implications and tests, and outline the need for future radiation-hydrodynamic modeling to predict demographics and detailed spectra.