General-relativistic structure of two-component quantum dark fermion stars

We develop a general-relativistic framework for two-component quantum dark fermion stars: equilibrium configurations of two degenerate fermion species governed by gravity, a Yukawa-mediated dark fifth force and a globally relevant Bohm quantum-pressure correction. The treatment retains the full covariant form of the nonlinear Klein--Gordon equation in the Schwarzschild interior, with closure relations valid at arbitrary compactness, from the ultralight baseline up to densities of order 0.16, fm-3 at which relativistic scalar densities and self-consistent effective fermion masses become unavoidable. Two Lagrangian parameters, the dark-fermion mass and the dimensionless ratio between the Yukawa channel and gravity, together fix the equilibrium structure; a joint measurement of mass and radius therefore constrains the dark-sector microphysics directly from gravitational-wave observables. For particle masses in the band 10-11 -- 10-10 eV, the configurations exhibit radii of 3 -- 24, km and compactness in the range 0.14 -- 0.34, behaving as dual mimickers: at moderate compactness they overlap with neutron stars in mass, radius, and inspiral frequency; at the most compact end (kappa about 0.34, R T/R S 1.5) they cross the photon sphere and could masquerade as low-mass black holes in the mass-gap region. Tidal-deformability measurements discriminate against both populations: the dimensionless tidal deformability is measurably smaller than the neutron-star value yet remains non-zero, unlike that of a genuine black hole. These objects populate the sensitivity bands of LISA, the Einstein Telescope, and Cosmic Explorer, producing astrometric microlensing signatures individually resolvable by Gaia. The framework thus provides a reproducible and falsifiable template for constraining dark-sector properties through multi-messenger observations.