We model long-term magneto-rotational evolution of isolated neutron stars (INSs) with long initial spin periods. This analysis is motivated by the recent discovery of young long-period neutron stars (NSs) observed as periodic radio sources: PSR J0901-4046, GLEAM-X J1627-52, and GPM J1839-10. Our calculations demonstrate that for realistically rapid spin-down during the propeller stage INSs with velocities ${\lesssim}100$ km s$^{-1}$ and assumed long initial spin periods can reach the stage of accretion from the interstellar medium within at most a few billion years as they are born already at the propeller stage or sufficiently close to the critical period of the ejector-propeller transition. If NSs with long initial spin periods form a relatively large fraction of all Galactic NSs then the number of isolated accretors is substantially larger than it has been predicted by previous studies.

In discussing open question in the field of massive stars, I consider their evolution from birth to death. After touching upon massive star formation, which may be bi-modal and not lead to a zero-age main sequence at the highest masses, I consider the consequences of massive stars being close to their Eddington limit. Then, when discussing the effects of a binary companion, I highlight the importance of massive Algols and contact binaries for understanding the consequences of mass transfer, and the role of binaries in forming Wolf-Rayet stars. Finally, a discussion on pair instability supernovae and of superluminous supernovae is provided.

Compact objects are of great interest in astrophysical research. There are active research interests in understanding better various aspects of formation and evolution of these objects. In this paper we addressed some problems related to the compact objects mass limit. We employed Einstein field equations (EFEs) to derive the equation of state (EoS). With the assumption of high densities and low temperature of compact sources, the derived equation of state is reduced to polytropic kind. Studying the polytropic equations we obtained similar physical implications, in agreement to previous works. Using the latest version of Mathematica-11 in our numerical analysis, we also obtained similar results except slight differences in accuracy.