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Massive $Δ$-resonance admixed hypernuclear stars with anti-kaon condensations

In this work, we study the effect of (anti)kaon condensation on the properties of compact stars that develop hypernuclear cores with and without an admixture of $Δ$-resonances. We work within the covariant density functional theory with the parameters adjusted to $K$-atomic and kaon-nucleon scattering data in the kaonic sector. The density-dependent parameters in the hyperonic sector are adjusted to the data on $Λ$ and $Ξ^-$ hypernuclei data. The $Δ$-resonance couplings are tuned to the data obtained from their scattering off nuclei and heavy-ion collision experiments. We find that (anti)kaon condensate leads to a softening of the equation of state and lower maximum masses of compact stars than in the absence of the condensate. Both the $K^-$ and $\bar K^0$-condensations occur through a second-order phase transition, which implies no mixed-phase formation. For large values of (anti)kaon and $Δ$-resonance potentials in symmetric nuclear matter, we observe that condensation leads to an extinction of $ Ξ^{-,0}$ hyperons. We also investigate the influence of inclusion of additional hidden-strangeness $σ^{*}$ meson in the functional and find that it leads to a substantial softening of the equation of state and delay in the onset of (anti)kaons.