In this work, we study the effect of differential rotation, finite temperature and strangeness on the quasi-stationary sequences of hyper-massive neutron stars. We generate constant rest-mass sequences of differentially rotating and uniformly rotating stars. The nucleonic matter relevant to the star interior is described within the framework of relativistic mean field model with the DD2 parameter set. We alsoconsider the strange $\Lambda$ hyperons using the BHB$\Lambda\phi$ equation of state (EoS). Additionally, we probe the behaviour of neutron stars (NS) with these compositions at different temperatures. We report that the addition of hyperons to the EoS, produces a significant boost to the spin-up phenomenon. Moreover,increasing the temperature can make the spin-up more robust. We also study the impact of strangeness and thermal effects on the T/W instability. Finally, we analyse the equilibrium sequences of a NS following a stable transition from differential rotation to uniform rotation. During this transition, the decrease in frequency relative to angular momentum loss is significantly smaller for EoS containing hyperons, compared tonucleonic EoS.

There are two types of timing irregularities seen in pulsars: glitches and timing noise. Both of these phenomena can help us to probe the interior of such exotic objects. This paper presents a brief overview of the observational and theoretical aspects of pulsar timing irregularities and the main results from the investigationsof these phenomena in India. The relevance of such Indian programs for monitoring of young pulsars with the square kilometer array (SKA) is presented, highlighting possible contributions of the Indian neutron star community to the upcoming SKA endeavor.

Decades long monitoring of millisecond pulsars, which exhibit highly stable rotational periods in pulsar timing array experiments is on the threshold of discovering nanohertz stochastic gravitational wave background. This paper describes the Indian pulsar timing array (InPTA) experiment, which employs the upgraded Giant Metrewave Radio Telescope (uGMRT) for timing an ensemble of millisecond pulsars for thispurpose. We highlight InPTA’s observation strategies and analysis methods, which are relevant for a future PTA experiment with the more sensitive Square Kilometer Array (SKA) telescope. We show that the unique multi-sub-array multi-band wide-bandwidth frequency coverage of the InPTA, provides dispersion measureestimates with unprecedented precision for PTA pulsars, e.g., $\sim$$2 \times 10^{−5}$ pc cm$^{−3}$ for PSR J1909-3744. Configuring the SKA-low and SKA-mid as two and four sub-arrays, respectively, it is shown that comparable precision is achievable, using observation strategies similar to those pursued by the InPTA, for a larger sample of 62 pulsars, requiring about 26 and 7 h per epoch for the SKA-mid and the SKA-low telescopes, respectively. We also review the ongoing efforts to develop PTA-relevant general relativistic constructs that will be required to search for nanohertz gravitational waves from isolated super-massive black hole binary systems like blazar OJ 287. These efforts should be relevant to pursue persistent multi-messenger gravitational wave astronomy during the forthcoming era of the SKA telescope, the thirty meter telescope, and the next-generation eventhorizon telescope.