Reaction-constrained composition g-modes in neutron stars with antikaon condensates, hyperons, and (1232) resonances

We study core composition g 1 modes of cold, nonrotating neutron stars containing antikaon condensates, hyperons, and (1232) baryons and present, to our knowledge, the first calculation in full general relativity of the continuous-composition g 1-mode frequency and gravitational-wave damping time for stars with a K- condensate. Using the BigApple relativistic mean-field equation of state, we compute frequencies, damping times, and frozen-composition tidal overlaps, and identify the buoyancy channels with a species-resolved Ledoux decomposition validated by mode-frequency sensitivities. We compare fully frozen matter with a fast- K limit for n p+K- and a strong-equilibrium limit for the quartet. Fast- K equilibration retains 36% -- 44% of the peak local kaon buoyancy and 65.7% -- 73.4% of the frozen terminal-configuration frequencies, while increasing the damping times by factors of 14.4 -- 31.8; the mode remains above the nucleonic band. Strong equilibration removes most of the direct-induced enhancement, returning the N mode toward the nucleonic band, whereas the high-frequency NY branch survives through the frozen gradient. Eigenfunction tracking confirms a continuous g 1 branch, and representative DD-ME2 calculations reproduce this hierarchy. The direct full-GR frozen-composition phase shifts satisfy g 1 at most1.410 times10-3 rad, a factor of 21 below the 0.03-rad favorable-event scale for the Einstein Telescope. An exotic species therefore produces a distinct composition mode only if its composition gradient, or a coupled slowly equilibrating gradient, survives over the oscillation period.