Abstract: In this study, we model a pulsar as a general relativistic oblique rotator, where the oblique rotator is a rotationally deformed neutron star whose rotation and magnetic axis are inclined at an angle. The oblique rotator spins down, losing rotational energy through the magnetic poles. The magnetic field is assumed to be dipolar; however, the star has a non-zero azimuthal component due to the misalignment. The magnetic field induces an electric field for a force-free condition. The magnetic field decreases as the misalignment increases and is minimum along the equatorial plane of the star. In contrast, the electric field remains almost constant initially but decreases rapidly at a high misalignment angle. The charge separation at the star surface is qualitatively similar to that of Newtonian calculation. We find that the power loss for a general relativistic rotator is minimum for either an aligned or an orthogonal rotator, which is in contrasts with Newtonian approach of calculation where the power loss increases with an increase in the misalignment angle.

Abstract: In this work we have analyzed the variation of speed of sound and trace anomaly inside a neutron star using neural network. We construct family of agnostic equation of state by maintaining thermodynamic stability, speed of sound bound with constraints from recent observation of neutron stars. The data of mass and radius serves an input for the neural network and we obtain speed of sound as an output. The speed of sound shows non-monotonic behaviour and the trained data predicts softer equation of state. The neural network predicts stiff equation of state at the centre of intermediate mass stars and massive stars have relatively softer equation of state at their centre. The trace anomaly shows a non-monotonic behaviour for the untrained data however, when we train our data; with neural network the trace anomaly shows monotonic behaviour and the condition of  Δ≥0  is maintained.

Abstract: Universal relations are important in testing many theories of physics. In the case of general relativity, we have the celebrated no-hair theorem for black holes. Unfortunately, the other compact stars, like neutron stars and white dwarfs, do not have such universal relation. However, neutron stars (and quark stars) have recently been found to follow certain universality, the I-Love-Q relations. These relations can provide a greater understanding of the structural and macro properties of compact astrophysical objects with knowledge of any one of the observables. The reason behind this is the lack of sensitivity to the relations with the equation of state of matter. In our present work, we have investigated the consistency of universal relations for a generic family of equations of state, which follows all the recent astrophysical constraints. Although the spread in the EoS is significant the universal nature of the trio holds relatively well up to a certain tolerance limit. The deviation from universality is seen to cross the tolerance limit with EoS, which is characteristically different from the original set.