No abstract

We study the effect of electric charge in compact stars assuming that the charge distribution is proportional to the mass density. The pressure and the density of the matter inside the stars are large, and the gravitational field is intense. This indicates that electric charge and a strong electric field can also be present. The relativistic hydrostatic equilibrium equation, i.e., the Tolman-Oppenheimer-Volkoff equation, is modified in order to include electric charge. We perform a detailed numerical study of the effect of electric charge using a polytropic equation of state. We conclude that in order to see any appreciable effect on the phenomenology of the compact stars, the electric fields have to be huge (∼ 10 21 V/m), which implies that the total charge is Q ∼ 10 20 Coulomb. From the local effect of the forces experienced on a single charged particle, it is expected that each individual charged particle is quickly ejected from the star. This in turn produces a huge force imbalance, and the gravitational force overwhelms the repulsive Coulomb and fluid pressure forces. The star can then collapse to form a charged black hole before all the charge leaves the system.

There are three categories of stars whose masses have been found accurately in recent times:(1) two for which Shapiro delay is used which is possible due to GR light bending as the partner is heavy : PSR J1614 − 2230 and PSR J1903+0327 (2) six eclipsing stars for which numerical Roche Lobe geometry is used and (3) 3 stars for which spectroscopic methods are used and in fact for these three the mass and radii both are estimated. Motivated by large color (N c ) expansion using a modified Richardson potential, along with density dependent quark masses thereby allowing chiral symmetry restoration, we get compact strange stars fitting all the observed masses.

We study the structure of neutron stars in the fðRÞ ¼ R þ αR 2 theory of gravity (the Starobinsky model) in an exact and nonperturbative approach. In this model, apart from the standard general relativistic junction conditions, two extra conditions-namely, the continuity of the curvature scalar and its first derivative-need to be satisfied. For an exterior Schwarzschild solution, the curvature scalar and its derivative must be zero at the stellar surface. We show that for some equation of state (EoS) of matter, matching all conditions at the surface of the star is impossible. Hence the model brings two major finetuning problems: (i) only some particular classes of EoS are consistent with Schwarzschild at the surface, and (ii) given the EoS, only a very particular set of boundary conditions at the center of the star will satisfy the given boundary conditions at the surface. Hence we show that this model [and subsequently many other fðRÞ models where the uniqueness theorem is valid] is highly unnatural for the existence of compact astrophysical objects. This is because the EoS of a compact star should be completely determined by the physics of nuclear matter at high density and not the theory of gravity.

The discovery of kilohertz quasi-periodic oscillations (kHz QPOs) in low-mass X-ray binaries (LMXBs) with the Rossi X-Ray Timing Explorer has stimulated extensive studies of these sources. Recently, Osherovich & Titarchuk suggested a new model for kHz QPOs and the related correlations between kHz QPOs and lowfrequency features in LMXBs. Here we use their results to study the mass-radius relation for the atoll source 4U 1728Ϫ34. We find that, if this model is correct, 4U 1728Ϫ34 is possibly a strange star rather than a neutron star.