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In this project, we try to find the correlation between the non-localpressure inside the massive neutron stars resisting the gravitational collapseof the core and ECSK dark energy led by the effect of spin-torsion couplingbetween quark fields and the space-time at very high densities much larger thanthe nuclear density. The injection of dark energy into the core of massiveneutron stars (MANs) and extra resistant nature of this dark energy to thecollapse of MANs by the anti-gravity give the possibility of existence ofneutron stars in the unobserved mass range of $[2.16M_{\odot},5M_{\odot}]$.Obtaining the ECSK TOV equation gives the local pressure of the ambient mediumof MANs. Moreover, the negative pressure from the ECSK dark energy is obtainedfrom the Lagrangian again, from which we are able to investigate thehydro-static equilibrium of the core and ambient medium of the MANs. If theequilibrium state is satisfied for the unobserved mass gap for the MANs in ECSKtheory framework this will imply our model predicts this vast mass range ofunobserved spectrum of the MANs in astrophysical studies.

Spin-Torsion effect on collapsing of first generation stars into neutron stars rather than black holes in Einstein-Cartan-Sciama-Kibble theory