Influence of dark matter induced by gravitational decoupling on maximum mass and stability of compact stars and understanding the mass gap phenomenon

ABSTRACT Recent gravitational wave events reported by the LIGO Livingston observatory and the LIGO–Virgo–KAGRA detector network point to the coalescing of a binary system comprising of a heaviest neutron star (NS) and the lightest black hole (BH) in the observable Universe. In this work, we provide a possible mechanism via gravitational decoupling and the contributions from dark matter (DM) to cast light on this so-called mass gap. In particular, we employ the Einasto spike and Bose–Einstein Condensate (BEC) DM profiles in conjunction with a generalized polytropic equation of state (EOS) and present two classes of solutions which describe self-gravitating objects. In order to achieve stable configurations which reside in the mass gap, we show that there is a sensitive interplay between the contributions from the DM normalization factor, the decoupling factor and interaction energy arising from the BEC. In particular, we find that the influence of the Einasto DM on the stellar configuration predicts a radius of $12.48^{+0.14}_{-0.12}$ km and the BEC DM accommodates a radius in the range of $13.13^{+0.09}_{-0.19}$ km to $13.69^{+0.04}_{-0.08}$ km consistent with the secondary companion of the GW190814 event. The tidal deformability of the NS and the Love number (LN) has been estimated, both of which set a constraint on the interaction strength $\alpha$ that quantify the effect of the DM background.