It is an exceptionally opportune time for astrophysics when a number of next-generation mega-instruments are poised to observe the Universe across the entire electromagnetic spectrum with unprecedented data quality. The Square Kilometre Array (SKA) is undoubtedly one of the major components of this scenario. In particular, the SKA is expected to discover tens of thousands of new neutron stars giving a major fillip to a wide range of scientific investigations. India has a sizeable community of scientists working on different aspects of neutron star physics with immediate access to both the uGMRT (an SKA pathfinder) and the recently launched X-ray observatory Astrosat. The current interests of the community largely centre around studies of (a) the generation of neutron stars and the SNe connection, (b) the neutron star population and evolutionary pathways, (c) the evolution of neutron stars in binaries and the magnetic fields, (d) the neutron star equation of state, (e) the radio pulsar emission mechanism, and (f) the radio pulsars as probes of gravitational physics. Most of these studies are the main goals of the SKA first phase, which is likely to be operational in the next four years. This article summarizes the science goals of the Indian neutron star community in the SKA era, with significant focus on coordinated efforts among the SKA and other existing/upcoming instruments.

We discuss different exotic phases and components of matter from the crust to the core of neutron stars based on theoretical models for equations of state relevant to core collapse supernova simulations and neutron star merger. Parameters of the models are constrained from laboratory experiments. It is observed that equations of state involving strangeness degrees of freedom such as hyperons and Bose–Einstein condensates are compatible with $2{M}_{\mathrm{solar}}$ neutron stars. The role of hyperons is explored on the evolution and stability of the protoneutron star in the context of SN1987A. Moment of inertia, mass and radius which are direct probes of neutron star interior are computed and their observational consequences are discussed. We continue our study on the dense matter under strong magnetic fields and its application to magnetoelastic oscillations of neutron stars.

Mass, radius and moment of inertia are direct probes of compositions and Equation of State (EoS) of dense matter in neutron star interior. These are computed for novel phases of dense matter involving hyperons and antikaon condensate and their observable consequences are discussed in this article. Furthermore, the relationship between moment of inertia and quadrupole moment is also explored.

Radio pulsars show remarkable clock-like stability, which make them useful astronomy tools in experiments to test equation of state of neutron stars and detecting gravitational waves using pulsar timing techniques. A brief review of relevant astrophysical experiments is provided in this paper highlighting thecurrent state-of-the-art of these experiments. A program to monitor frequently glitching pulsars with Indian radio telescopes using high cadence observations is presented, with illustrations of glitches detected in this program, including the largest ever glitch in PSR B0531 $+$ 21. An Indian initiative to discover sub-$\mu$Hz gravitational waves, called Indian Pulsar Timing Array (InPTA), is also described briefly, where time-of-arrival uncertainties and post-fit residuals of the order of $\mu$s are already achievable, comparable to other international pulsar timing array experiments. While timing the glitches and their recoveries are likely to provide constraints on the structure of neutron stars, InPTA will provide upper limits on sub-$\mu$Hz gravitational waves apart from auxiliary pulsarscience. Future directions for these experiments are outlined.