We develop a general formalism to treat, in general relativity, the linear oscillations of a twofluid star about static (non-rotating) configurations. Such a formalism is intended for neutron stars, whose matter content can be described, as a first approximation, by a two-fluid model: one fluid is the neutron superfluid, which is believed to exist in the core and inner crust of mature neutron stars; the other fluid is a conglomerate of all other constituents (crust nuclei, protons, electrons, etc...). We obtain a system of equations which govern the perturbations both of the metric and of the matter variables, whatever the equation of state for the two fluids. As a first application, we consider the simplified case of two non-interacting fluids, each with a polytropic equation of state. We compute numerically the quasi-normal modes (i.e. oscillations with purely outgoing gravitational radiation) of the corresponding system. When the adiabatic indices of the two fluids are different, we observe a splitting for each frequency of the analogous single fluid spectrum. The analysis also substantiates the claim that w-modes are largely due to spacetime oscillations.

We propose here a robust scheme to infer the physical parameters of compact stars from their fmode gravitational wave signals. We first show that the frequency and the damping rate of f-mode oscillation of compact stars can be expressed in terms of universal functions of stellar mass and moment of inertia. By employing the universality in the f-mode one can then infer accurate values of the mass, the moment of inertia and the radius of a compact star. In addition, we demonstrate that our new scheme works well for both realistic neutron stars and quark stars, and hence provides a unifying way to infer the physical parameters of compact stars.

We study the dimensionless spin parameter j (= cJ/(GM 2 )) of uniformly rotating neutron stars and quark stars in general relativity. We show numerically that the maximum value of the spin parameter of a neutron star rotating at the Keplerian frequency is j max ∼ 0.7 for a wide class of realistic equations of state. This upper bound is insensitive to the mass of the neutron star if the mass of the star is larger than about 1 M ⊙ . On the other hand, the spin parameter of a quark star modeled by the MIT bag model can be larger than unity and does not have a universal upper bound. Its value also depends strongly on the bag constant and the mass of the star. Astrophysical implications of our finding will be discussed.

We study the dynamical evolution of a large amplitude r-mode by numerical simulations. R-modes in neutron stars are unstable growing modes, driven by gravitational radiation reaction. In these simulations, r-modes of amplitude unity or above are destroyed by a catastrophic decay: A large amplitude r-mode gradually leaks energy into other fluid modes, which in turn act nonlinearly with the r-mode, leading to the onset of the rapid decay. As a result the r-mode suddenly breaks down into a differentially rotating configuration. The catastrophic decay does not appear to be related to shock waves at the star's surface. The limit it imposes on the r-mode amplitude is significantly smaller than that suggested by previous fully nonlinear numerical simulations.

We study the hydrostatic equilibrium configuration of an admixture of degenerate dark matter and normal nuclear matter by using a general relativistic two-fluid formalism. We consider non-selfannihilating dark matter particles of mass $1 GeV. The mass-radius relations and moments of inertia of these dark-matter admixed neutron stars are investigated and the stability of these stars is demonstrated by performing a radial perturbation analysis. We find a new class of compact stars which consists of a small normal matter core with radius of a few kilometers embedded in a ten-kilometer-sized dark matter halo. These stellar objects may be observed as extraordinarily small neutron stars that are incompatible with realistic nuclear matter models.

Though individual stellar parameters of compact stars usually demonstrate obvious dependence on the equation of state (EOS), EOS-insensitive universal formulas relating these parameters remarkably exist. In the present paper, we explore the interrelationship between two such formulas, namely the f -I relation connecting the f -mode quadrupole oscillation frequency ω2 and the moment of inertia I, and the I-Love-Q relations relating I, the quadrupole tidal deformability λ2, and the quadrupole moment Q, which have been proposed by Lau, Leung, and Lin [Astrophys. J. 714, 1234 (2010)] and Yagi and Yunes [Science 341, 365 (2013)], respectively. A relativistic universal relation between ω l and λ l with the same angular momentum l = 2, 3, . . ., the so-called "diagonal f -Love relation" that holds for realistic compact stars and stiff polytropic stars, is unveiled here. An in-depth investigation in the Newtonian limit is further carried out to pinpoint its underlying physical mechanism and hence leads to a unified f -I-Love relation. We reach the conclusion that these EOS-insensitive formulas stem from a common physical origin -compact stars can be considered as quasiincompressible when they react to slow time variations introduced by f -mode oscillations, tidal forces and rotations.

Due to our ignorance of the equation of state (EOS) beyond nuclear density, there is still no unique theoretical model for neutron stars (NSs). It is therefore surprising that universal EOS-independent relations connecting different physical quantities of NSs can exist. Lau et al. found that the frequency of the f -mode oscillation, the mass, and the moment of inertia are connected by universal relations. More recently, Yagi and Yunes discovered the I-Love-Q universal relations among the mass, the moment of inertia, the Love number, and the quadrupole moment. In this paper, we study these universal relations in the Eddington-inspired Born-Infeld (EiBI) gravity. This theory differs from general relativity (GR) significantly only at high densities due to the nonlinear coupling between matter and gravity. It thus provides us an ideal case to test how robust the universal relations of NSs are with respect to the change of the gravity theory. Thanks to the apparent EOS formulation of EiBI gravity developed recently by Delsate and Steinhoff, we are able to study the universal relations in EiBI gravity using the same techniques as those in GR. We find that the universal relations in EiBI gravity are essentially the same as those in GR. Our work shows that, within the currently viable coupling constant, there exists at least one modified gravity theory that is indistinguishable from GR in view of the unexpected universal relations. Subject headings: dense matter -equation of state -stars: neutron

We study the hydrostatic equilibrium structure of compact stars in the Eddington-inspired BornInfeld gravity recently proposed by Bañados and Ferreira [Phys. Rev. Lett. 105, 011101 (2010)]. We also develop a framework to study the radial perturbations and stability of compact stars in this theory. We find that the standard results of stellar stability still hold in this theory. The frequency square of the fundamental oscillation mode vanishes for the maximum-mass stellar configuration. The dependence of the oscillation mode frequencies on the coupling parameter κ of the theory is also investigated. We find that the fundamental mode is insensitive to the value of κ, while higher-order modes depend more strongly on κ.