Abstract. In this article we study the hydrostatic equilibrium configuration of neutron stars and strange stars, whose fluid pressure is computed from the equations of state p = ωρ 5/3 and p = 0.28(ρ − 4B), respectively, with ω and B being constants and ρ the energy density of the fluid. We start by deriving the hydrostatic equilibrium equation for the f (R, T ) theory of gravity, with R and T standing for the Ricci scalar and trace of the energy-momentum tensor, respectively. Such an equation is a generalization of the one obtained from general relativity, and the latter can be retrieved for a certain limit of the theory. For the f (R, T ) = R + 2λT functional form, with λ being a constant, we find that some physical properties of the stars, such as pressure, energy density, mass and radius, are affected when λ is changed. We show that for a fixed central star energy density, the mass of neutron and strange stars can increase with λ. Concerning the star radius, it increases for neutron stars and it decreases for strange stars with the increment of λ. Thus, in f (R, T ) theory of gravity we can push the maximum mass above the observational limits. This implies that the equation of state cannot be eliminated if the maximum mass within General Relativity lies below the limit given by observed pulsars.arXiv:1511.06282v2 [gr-qc]

We explore a class of compact charged spheres made of a charged perfect fluid with a polytropic equation of state. The charge density is chosen to be proportional to the energy density. The study is performed by solving the Tolman-Oppenheimer-Volkoff (TOV) equation which describes the hydrostatic equilibrium. We show the dependence of the structure of the spheres for several characteristic values of the polytropic exponent and for different values of the charge densities. We also study other physical properties of the charged spheres, such as the total mass, total charge, radius and sound speed and their dependence on the polytropic exponent. We find that for the polytropic exponent γ = 4/3 the Chandrasekhar mass limit coincides with the Oppenheimer-Volkoff mass limit. We test the Oppenheimer-Volkoff limit for such compact objects. We also analyze the Buchdahl limit for these charged polytropic spheres, which happens in the limit of very high polytropic exponents, i.e., for a stiff equation of state. It is found that this limit is extremal and it is a quasiblack hole.

The hydrostatic equilibrium and the stability against radial perturbation of charged strange quark stars composed of a charged perfect fluid are studied. For this purpose, it is considered that the perfect fluid follows the MIT bag model equation of state and the radial charge distribution follows a power-law. The hydrostatic equilibrium and the stability of charged strange stars are investigated through the numerical solutions of the Tolman-Oppenheimer-Volkoff equation and the Chandrasekhar's pulsation equation, being these equations modified from their original form to include the electrical charge. In order to appreciably affect the stellar structure, it is found that the total charge should be of order 10 20 [C], implying an electric field of around 10 22 [V/m]. We found the electric charge that produces considerable effect on the structure and stability of the object is close to the star's surface. We obtain that for a range of central energy density the stability of the star decreases with the increment of the total charge and for a range of total mass the electric charge helps to grow the stability of the stars under study. We show that the central energy density used to reach the maximum mass value is the same used to determine the zero eigenfrequency of the fundamental mode when the total charge is fixed, thus indicating that the maximum mass point marks the onset of instability. In other words, when fixing the total charge, the conditions dM dρc > 0 and dM dρc < 0 are necessary and sufficient to determine the stable and unstable equilibrium configurations regions against radial oscillations. We also consider another charge distribution, charge density proportional to the energy density, and show that our results do not depend on this choice and the conditions used to determine regions made of the stable and unstable charged equilibrium configurations are maintained.

In this work we investigate the equilibrium configurations of white dwarfs in a modified gravity theory, namely, f (R, T ) gravity, for which R and T stand for the Ricci scalar and trace of the energy-momentum tensor, respectively. Considering the functional form f (R, T ) = R +2λT , with λ being a constant, we obtain the hydrostatic equilibrium equation for the theory. Some physical properties of white dwarfs, such as: mass, radius, pressure and energy density, as well as their dependence on the parameter λ are derived. More massive and larger white dwarfs are found for negative values of λ when it decreases. The equilibrium configurations predict a maximum mass limit for white dwarfs slightly above the Chandrasekhar limit, with larger radii and lower central densities when compared to standard gravity outcomes. The most important effect of f (R, T ) theory for massive white dwarfs is the increase of the radius in comparison with GR and also f (R) results. By comparing our results with some observational data of massive white dwarfs we also find a lower limit for λ, namely, λ > −3 × 10 −4 .

Abstract. The influence of the anisotropy in the equilibrium and stability of strange stars is investigated through the numerical solution of the hydrostatic equilibrium equation and the radial oscillation equation, both modified from their original version to include this effect. The strange matter inside the quark stars is described by the MIT bag model equation of state. For the anisotropy two different kinds of local anisotropic σ = p t − p r are considered, where p t and p r are respectively the tangential and the radial pressure: one that is null at the star's surface defined by p r (R) = 0, and one that is nonnull at the surface, namely, σ s = 0 and σ s = 0. In the case σ s = 0, the maximum mass value and the zero frequency of oscillation are found at the same central energy density, indicating that the maximum mass marks the onset of the instability. For the case σ s = 0, we show that the maximum mass point and the zero frequency of oscillation coincide in the same central energy density value only in a sequence of equilibrium configurations with the same value of σ s . Thus, the stability star regions are determined always by the condition dM/dρ c > 0 only when the tangential pressure is maintained fixed at the star surface's p t (R). These results are also quite important to analyze the stability of other anisotropic compact objects such as neutron stars, boson stars and gravastars.arXiv:1607.03984v2 [astro-ph.HE]