The recent detection of pulsations from the ultra luminous X-ray source (ULX) NuSTAR J095551+6940.8 in M82 by Bachetti et al. indicates that the object is an accreting neutron star in a high mass X-ray binary (HMXB) system. The superEddington luminosity of the object implies that the magnetic field is sufficiently strong to suppress the scattering cross-section unless its beam is viewed at a favourable angle. We show that the torque equilibrium condition for the pulsar indicates the dipole magnetic field of the neutron star is 6.7 × 10 13 G, two orders of magnitude higher than that estimated by Bachetti et al., and further point to the possibility that even stronger magnetic fields could well be in the higher multipoles. This supports the recent view that magnetars descent from HMXBs if the magnetic field decays an order of magnitude during the process of transition.

Deviations from the predictions of general relativity due to energy-momentum squared gravity (EMSG) are expected to become pronounced in the high density cores of neutron stars. We derive the hydrostatic equilibrium equations in EMSG and solve them numerically to obtain the neutron star mass-radius relations for four different realistic equations of state. We use the existing observational measurements of the masses and radii of neutron stars to constrain the free parameter, α, that characterizes the coupling between matter and spacetime in EMSG. We show that −10 −38 cm 3 /erg < α < +10 −37 cm 3 /erg. Under this constraint, we discuss what contributions EMSG can provide to the physics of neutron stars, in particular, their relevance to the so called hyperon puzzle in neutron stars. We also discuss how EMSG alters the dynamics of the early universe from the predictions of the standard cosmological model. We show that EMSG leaves the standard cosmology safely unaltered back to t ∼ 10 −4 seconds at which the energy density of the universe is ∼ 10 34 erg cm −3 .

The recently discovered rotationally powered pulsar PSR J1640-4631 is the first to have a braking index measured, with high enough precision, that is greater than three. An inclined magnetic rotator in vacuum or plasma would be subject not only to spin-down but also to an alignment torque. The vacuum model can address the braking index only for an almost orthogonal rotator that is incompatible with the single peaked pulse profile. The magnetic dipole model with the corotating plasma predicts braking indices between 3 − 3.25. We find that the braking index of 3.15 is consistent with two different inclination angles, 18.5 ± 3 degrees and 56 ± 4 degrees. The smaller angle is preferred given the pulse profile has a single peak and the radio output of the source is weak. We infer the change in the inclination angle to be at the rate −0.23 degrees per century, three times smaller in absolute value than the rate recently observed for the Crab pulsar.

We study the structure of relativistic stars in R + αR 2 theory using the method of matched asymptotic expansion to handle the higher order derivatives in field equations arising from the higher order curvature term. We find solutions, parametrized by α, for uniform density stars. We obtain the mass-radius relations and study the dependence of maximum mass on α. We find that Mmax is almost linearly proportional to α. For each α the maximum mass configuration has the biggest compactness parameter (η = GM/Rc 2 ), and we argue that the general relativistic stellar configuration corresponding to α = 0 is the least compact among these.

The vacuum solutions around a spherically symmetric and static object in the Starobinsky model are studied with a perturbative approach. The differential equations for the components of the metric and the Ricci scalar are obtained and solved by using the method of matched asymptotic expansions. The presence of higher order terms in this gravity model leads to the formation of a boundary layer near the surface of the star allowing the accommodation of the extra boundary conditions on the Ricci scalar. Accordingly, the metric can be different from the Schwarzschild solution near the star depending on the value of the Ricci scalar at the surface of the star while matching the Schwarzschild metric far from the star.