Neutron stars provide an excellent laboratory for physics under the most extreme conditions. Up to now, models of axisymmetric, stationary, differentially rotating neutron stars were constructed under the strong assumption of barotropicity, where a one-to-one relation between all thermodynamic quantities exists. This implies that the specific angular momentum of a matter element depends only on its angular velocity. The physical conditions in the early stages of neutron stars, however, are determined by their violent birth processes, typically a supernova or in some cases the merger of two neutron stars, and detailed numerical models show that the resulting stars are by no means barotropic. Here, we construct models for stationary, differentially rotating, non-barotropic neutron stars, where the equation of state and the specific angular momentum depend on more than one independent variable. We show that the potential formulation of the relativistic Euler equation can be extended to the non-barotropic case, which, to the best of our knowledge, is a new result even for the Newtonian case. We implement the new method into the XNS code and construct equilibrium configurations for non-barotropic equations of state. We scrutinize the resulting configurations by evolving them dynamically with the numerical relativity code BAM, thereby demonstrating that the new method indeed produces stationary, differentially rotating, non-barotropic neutron star configurations.
We develop a numerical scheme for obtaining the $r$-mode oscillations of rapidly rotating relativistic stars. In the present scheme, we neglect all metric perturbations and only take account of the dynamics of the fluid in the background spacetime of the unperturbed star (the relativistic Cowling approximation). We also assume the star is barotropic, i.e. neutrally stable against convection under the assumption of adiabatic oscillations. Our numerical scheme is based on the Yoshida-Eriguchi formulation for the analysis of the general relativistic f-mode oscillations in the Cowling approximatio…
With (non-barotropic) equations of state valid even when the neutron, proton and electron content of neutron star cores is not in beta equilibrium, we study inertial and composition gravity modes of relativistic rotating neutron stars. We solve the relativistic Euler equations in the time domain with a three dimensional numerical code based on spectral methods, in the slow rotation, relativistic Cowling and anelastic approximations. Principally, after a short description of the gravity modes due to smooth composition gradients, we focus our analysis on the question of how the inertial modes ar…
We cut and paste two Banados-Teitelboim-Zanelli (BTZ) spacetimes at a throat by the Darmois-Israel method to construct a rotating wormhole with a thin shell filled with a barotropic fluid. The thin shell at the throat and both sides of the throat corotate. We investigate the linear stability of the thin shell of the rotating wormhole against radial perturbations. We show that the wormhole becomes more and more stable the larger its angular momentum is until the angular momentum reaches a critical value and that the behavior of a condition for stability significantly changes when the angular mo…
The axial mode oscillations are examined for relativistic rotating stars with uniform angular velocity. Using the slow rotation formalism and the Cowling approximation, we have derived the equations governing the r-mode oscillations up to the second order with respect to the rotation. In the lowest order, the allowed range of the frequencies is determined, but corresponding spatial function is arbitrary. The spatial function can be decomposed in non-barotropic region by a set of functions associated with the differential equation of the second-order corrections. The equation however becomes si…
In the last few decades, lots of universal relations between different global physical quantities of neutron stars have been proposed to constrain the unobservable or hard to be observed properties of neutron stars. But few of them are related to the gravitational redshift or the gravitational binding energy, especially for the fast rotating neutron stars. Here we will focus on the universal relations related to these two quantities. Based on 11 equations of state (EOSs) from the predictions of microscopic nuclear many-body theories for normal or hybrid neutron stars, we proposed a set of new …
The spherically symmetric thin shells of the barotropic fluids with the linear equation of state are considered within the frameworks of general relativity. We study several aspects of the shells as completely relativistic models of stars, first of all the neutron stars and white dwarfs, and circumstellar shells. The exact equations of motion of the shells are obtained. Also we calculate the parameters of the equilibrium configurations, including the radii of static shells. Finally, we study the stability of the equilibrium shells against radial perturbations.
The \lq\lq effective geometry" formalism is used to study the perturbations of a perfect barotropic Newtonian self-gravitating rotating and compressible fluid coupled with gravitational backreaction. The case of a uniformly rotating polytrope with index $n=1$ is investigated, due to its analytical tractability. Special attention is devoted to the geometrical properties of the underlying background acoustic metric, focusing in particular on null geodesics as well as on the analog light cone structure.
Methods are developed for constructing spectral representations of cold (barotropic) neutron-star equations of state. These representations are faithful in the sense that every physical equation of state has a representation of this type, and conversely every such representation satisfies the minimal thermodynamic stability criteria required of any physical equation of state. These spectral representations are also efficient, in the sense that only a few spectral coefficients are generally required to represent neutron-star equations of state quiet accurately. This accuracy and efficiency is i…
The stability properties of relativistic stars against gravitational collapse to black hole is a classical problem in general relativity. A sufficient criterion for secular instability was established by Friedman, Ipser and Sorkin (1988), who proved that a sequence of uniformly rotating barotropic stars is secularly unstable on one side of a turning point and then argued that a stronger result should hold: that the sequence should be stable on the opposite side, with the turning point marking the onset of secular instability. We show here that this expectation is not met. By computing in full …
Rotation causes an increase in a neutron star's mass and equatorial radius. The mass and radius depend sensitively on the unknown equation of state (EOS) of cold, dense matter. However, the increases in mass and radius due to rotation are almost independent of the EOS. The EOS independence leads to the idea of neutron star universality. In this paper, we compute sequences of rotating neutron stars with constant central density. We use a collection of randomly generated EOS to construct simple correction factors to the mass and radius computed from the equations of hydrostatic equilibrium for n…
The Neutron star Interior Composition Explorer (NICER) is currently observing the x-ray pulse profiles emitted by hot spots on the surface of rotating neutron stars allowing for an inference of their radii with unprecedented precision. A critical ingredient in the pulse profile model is an analytical formula for the oblate shape of the star. These formulas require a fitting over a large ensemble of neutron star solutions, which cover a wide set of equations of state, stellar compactnesses and rotational frequencies. However, this procedure introduces a source of systematic error, as (i) the fi…
We construct a new three-dimensional general relativistic magnetohydrodynamics code, in which a fixed mesh refinement technique is implemented. To ensure the divergence-free condition as well as the magnetic flux conservation, we employ the method by Balsara (2001). Using this new code, we evolve differentially rotating magnetized neutron stars, and find that a magnetically driven outflow is launched from the star exhibiting a kink instability. The matter ejection rate and Poynting flux are still consistent with our previous finding (Shibata et al., 2011) obtained in axisymmetric simulations.
$f(R)$ theories of gravity are one of the most popular alternative explanations for dark energy and therefore studying the possible astrophysical implications of these theories is an important task. In the present paper we make a substantial advance in this direction by considering rapidly rotating neutron stars in $R^2$ gravity. The results are obtained numerically and the method we use is non-perturbative and self-consistent. The neutron star properties, such as mass, radius and moment of inertia, are studied in detail and the results show that rotation magnifies the deviations from general …
The opportunity to study physics at supra-nuclear densities through X-ray observations of neutron stars has led to in-depth investigations of certain approximately universal relations that can remove degeneracies in pulse profile models. One such set of relations determines all of the multipole moments of a neutron star just from the first three (the mass monopole, the current dipole and the mass quadrupole moment) approximately independently of the equation of state. These three-hair relations were found to hold in neutron stars that rotate rigidly, as is the case in old pulsars, but neutron …
Recently it was shown that slowly rotating neutron stars exhibit an interesting correlation between their moment of inertia $I$, their quadrupole moment $Q$, and their tidal deformation Love number $λ$ (the I-Love-Q relations), independently of the equation of state of the compact object. In the present work a similar, more general, universality is shown to hold true for all rotating neutron stars within General Relativity; the first four multipole moments of the neutron star are related in a way independent of the nuclear matter equation of state we assume. By exploiting this relation, we can…
We investigate the dynamical stability of relativistic, differentially rotating, quasi-toroidal models of neutron stars through hydrodynamical simulations in full general relativity. We find that all quasi-toroidal configurations studied in this work are dynamically unstable against the growth of non-axisymmetric modes. Both one-arm and bar mode instabilities grow during their evolution. We find that very high rest mass configurations collapse to form black holes. Our calculations suggest that configurations whose rest mass is less than the binary neutron star threshold mass for prompt collaps…
We present the field equations governing the equilibrium of rapidly rotating neutron stars in scalar-tensor theories of gravity, as well as representative numerical solutions. The conditions for the presence of a nontrivial scalar field and the deviations from the general relativistic solutions are studied. Two examples of scalar-tensor theories are examined - one case that is equivalent to the Brans-Dicke theory and a second case, that is perturbatively equivalent to Einstein's General Relativity in the weak field regime, but can differ significantly for strong fields. Our numerical results s…
Viscosity driven bar mode secular instabilities of rapidly rotating neutron stars are studied using LORENE/Nrotstar code. These instabilities set a more rigorous limit to the rotation frequency of neutron star than the Kepler frequency/mass shedding limit. The procedure employed in the code comprises of perturbing an axisymmetric and stationary configuration of a neutron star and studying its evolution by constructing a series of triaxial quasi-equilibrium configurations. Symmetry breaking point was found out for Polytropic as well as 10 realistic Equations of states (EOS) from the CompOSE dat…
We perform the first magnetohydrodynamic simulations in full general relativity of self-consistent rotating neutron stars (NSs) with ultrastrong mixed poloidal and toroidal magnetic fields. The initial uniformly rotating NS models are computed assuming perfect conductivity, stationarity, and axisymmetry. Although the specific geometry of the mixed field configuration can delay or accelerate the development of various instabilities known from analytic perturbative studies, all our models finally succumb to them. Differential rotation is developed spontaneously in the cores of our magnetars whic…
We investigate the Keplerian (mass-shedding) sequence of rotating neutron stars. Twelve different equations of state are used to describe the nuclear structure. We find four fitting relations which connect the rotating frequency, mass and radius of stars in the mass-shedding limit to the mass and radius of stars in the static sequence. We show the breakdown of approximate relation for the Keplerian frequency derived by Lattimer and Prakash [Science, 304, 536, (2004)] and then we present a new, EOS-independent and more accurate relation. This relation fits the Keplerian frequency of rotating ne…
In the present paper we investigate self-consistently slowly rotating neutron and strange stars in R-squared gravity. For this purpose we first derive the equations describing the structure of the slowly rotating compact stars in $f(R)$-gravity and then simultaneously solve the exterior and the interior problem. The structure of the slowly rotating neutron stars is studied for two different hadronic equations of state and a strange matter equation of state. The moment of inertia and its dependence on the stellar mass and the $R$-squared gravity parameter $a$ is also examined in details. We fin…
Plasma magnetosphere surrounding rotating magnetized neutron star in the braneworld has been studied. For the simplicity of calculations Goldreich-Julian charge density is analyzed for the aligned neutron star with zero inclination between magnetic field and rotation axis. From the system of Maxwell equations in spacetime of slowly rotating star in braneworld, second-order differential equation for electrostatic potential is derived. Analytical solution of this equation indicates the general relativistic modification of an accelerating electric field and charge density along the open field lin…
Hartle's model for slowly rotating stars has been extensively used to compute equilibrium configurations of slowly rotating stars to second order in perturbation theory in General Relativity, given a barotropic equation of state (EOS). A recent study based on the modern theory of perturbed matchings show that the model must be amended to accommodate EOS's in which the energy density does not vanish at the surface of the non rotating star. In particular, the expression for the change in mass given in the original model, i.e. a contribution to the mass that arises when the perturbations are chos…
We study the inertial modes of slowly rotating, fully relativistic compact stars. The equations that govern perturbations of both barotropic and non-barotropic models are discussed, but we present numerical results only for the barotropic case. For barotropic stars all inertial modes are a hybrid mixture of axial and polar perturbations. We use a spectral method to solve for such modes of various polytropic models. Our main attention is on modes that can be driven unstable by the emission of gravitational waves. Hence, we calculate the gravitational-wave growth timescale for these unstable mod…
This note describes fitting formulae for the gravitational waveforms generated by a rapidly rotating neutron star (e.g., newly-formed in the core collapse of a supernova) as it evolves from an initial axisymmetric configuration toward a triaxial ellipsoid.
We demonstrate a possibility of existence of a peculiar temperature-dependent composition $g$-modes in superfluid neutron stars. We calculate the Brunt-V$\ddot{\rm a}$is$\ddot{\rm a}$l$\ddot{\rm a}$ frequency for these modes, as well as their eigenfrequencies. The latter turn out to be rather large, up to $\sim 500$ Hz for a chosen model of a neutron star. This result indicates, in particular, that use of the barotropic equation of state may be not a good approximation for calculation of inertial modes even in most rapidly rotating superfluid neutron stars.
In this chapter we review the recent results on the equilibrium configurations of static and uniformly rotating neutron stars within the Hartle formalism. We start from the Einstein-Maxwell-Thomas-Fermi equations formulated and extended by Belvedere et al. (2012, 2014). We demonstrate how to conduct numerical integration of these equations for different central densities ${\it ρ}_c$ and angular velocities $Ω$ and compute the static $M^{stat}$ and rotating $M^{rot}$ masses, polar $R_p$ and equatorial $R_{\rm eq}$ radii, eccentricity $ε$, moment of inertia $I$, angular momentum $J$, as well as t…
Neutron stars are among the densest known objects in the universe and an ideal laboratory for the strange physics of super-condensed matter. While the simultaneously measurements of mass and radius of non-rotating neutron stars may impose constraints on the properties of the dense nuclear matter, the observation and study of maximally-rotating ones, close to the mass-shedding limit, may lead to significantly further constraints. Theoretical predictions allow neutron stars to rotate extremely fast (even more than $2000 \ {\rm Hz}$). However, until this moment, the fastest observed rotating puls…
Using a fully general relativistic implementation of ideal magnetohydrodynamics with no assumed symmetries in three spatial dimensions, the dynamics of magnetized, rigidly rotating neutron stars are studied. Beginning with fully consistent initial data constructed with Magstar, part of the Lorene project, we study the dynamics and stability of rotating, magnetized polytropic stars as models of neutron stars. Evolutions suggest that some of these rotating, magnetized stars may be minimally unstable occurring at the threshold of black hole formation.
We present rapidly rotating neutron stars featuring wormholes in their centers. They arise in general relativity in the presence of a ghost scalar field. The nuclear matter is described by a polytropic equation of state, yielding realistic masses and radii for the neutron stars. The wormholes possess small circumferential radii of size up to 3 km. With increasing wormhole size, the masses and radii of the stars decrease, while the domain of existence of these rotating mixed neutron-star-plus-wormhole systems retains the characteristic properties of a rotating neutron star domain. The question …
Employing a simplified version of the Israel-Stewart formalism for general-relativistic shear-viscous hydrodynamics, we perform axisymmetric general-relativistic simulations for a rotating neutron star surrounded by a massive torus, which can be formed from differentially rotating stars. We show that with our choice of a shear-viscous hydrodynamics formalism, the simulations can be stably performed for a long time scale. We also demonstrate that with a possibly high shear-viscous coefficient, not only viscous angular momentum transport works but also an outflow could be driven from a hot envel…
The equations describing nonradial adiabatic oscillations of differentially rotating relativistic stars are derived in relativistic slow rotation approximation. The differentially rotating configuration is described by a perturbative version of the relativistic j-constant rotation law. Focusing on the oscillation properties of the stellar fluid, the adiabatic nonradial perturbations are studied in the Cowling approximation with a system of five partial differential equations. In these equations, differential rotation introduces new coupling terms between the perturbative quantites with respect…
This work is devoted to the construction of slowly rotating neutron stars in the framework of the nonminimal derivative coupling sector of Horndeski theory. We match the large radius expansion of spherically symmetric solutions with cosmological solutions and we find that the most viable model has only one free parameter. Then, by using several tabulated and realistic equations of state, we establish numerically the upper bound for this parameter in order to construct neutron stars in the slow rotation approximation with the maximal mass observed today. We finally study the surface redshift an…
We investigate equilibrium configurations of uniformly rotating neutron stars in $R^2$ gravity with axion scalar field for GM1 equation of state (EoS) for nuclear matter. The mass-radius diagram, mass-central energy density are presented for some frequencies in comparison with static stars. We also compute equatorial and polar radii and moment of inertia for stars. For axion field $ϕ$ the coupling in the form $\sim R^2ϕ$ is assumed. Several interesting results follow from our consideration. Maximal possible star mass with given EoS increases due to the contribution of coupling term. We discove…
In the present paper we examine gravitational wave asteroseismology relations for f-modes of rapidly rotating neutron stars. An approach different to the previous studies is employed - first, the moment of inertia is used instead of the stellar radius, and second, the normalization of the oscillation frequencies and damping times is different. It was shown that in the non-rotating case this can lead to a much stronger equation of state independence and our goal is to generalize the static relations to the rapidly rotating case and values of the spherical mode number $l\ge2$. We employ realisti…
We construct sequences of rapidly rotating neutron stars in dilatonic Einstein-Gauss-Bonnet theory, employing two equations of state for the nuclear matter. We analyze the dependence of the physical properties of these neutron stars on the Gauss-Bonnet coupling strength. For a given equation of state we determine the physically relevant domain of rapidly rotating neutron stars, which is delimited by the set of neutron stars rotating at the Kepler limit, the set of neutron stars along the secular instability line, and the set of static neutron stars. As compared to Einstein gravity, the presenc…
Neutron stars are attractive places to look for dark matter because their high densities allow repeated interactions. Weakly interacting massive particles (WIMPs) may scatter efficiently in the core or in the crust of a neutron star. In this paper we focus on WIMP contributions to transport properties, such as shear viscosity or thermal conductivity, because these can be greatly enhanced by long mean free paths. We speculate that WIMPs increase the shear viscosity of neutron star matter and help stabilize r-mode oscillations. These are collective oscillations where the restoring force is the C…
In this work we provide a framework that connects the co-rotating and counter rotating $f$-mode frequencies of rotating neutron stars with their stellar structure. The accurate computation of these modes for realistic equations of state has been presented recently and they are here used as input for a Bayesian analysis of the inverse problem. This allows to quantitatively reconstruct basic neutron star parameters, such as the mass, radius, rotation rate or universal scaling parameters. We find that future observations of both $f$-mode frequencies, in combination with a Bayesian analysis, would…
A four-parameter class of exact asymptotically flat solutions of the Einstein-Maxwell equations involving only rational functions is presented. It is able to describe the exterior field of a slowly or rapidly rotating neutron star with poloidal magnetic field.
We construct relativistic equilibrium models of differentially rotating neutron stars and show that they can support significantly more mass than their nonrotating or uniformly rotating counterparts. We dynamically evolve such ``hypermassive'' models in full general relativity and show that there do exist configurations which are dynamically stable against radial collapse and bar formation. Our results suggest that the remnant of binary neutron star coalescence may be temporarily stabilized by differential rotation, leading to delayed collapse and a delayed gravitational wave burst.
In this review we summarize the current understanding of the gravitational-wave driven instability associated with the so-called r-modes in rotating neutron stars. We discuss the nature of the r-modes, the detailed mechanics of the instability and its potential astrophysical significance. In particular we discuss results regarding the spin-evolution of nascent neutron stars, the detectability of r-mode gravitational waves and mechanisms limiting the spin-rate of accreting neutron stars in binary systems.
A new spectral code for constructing general-relativistic models of rapidly rotating stars with an unprecedented accuracy is presented. As a first application, we reexamine uniformly rotating homogeneous stars and compare our results with those obtained by several previous codes. Moreover, representative relativistic examples corresponding to highly flattened rotating bodies are given.
We study oscillations of slowly rotating relativistic barotropic as well as non-barotropic polytropic stars in the Cowling approximation, including first order rotational corrections. By taking into account the coupling between the polar and axial equations, we find that, in contrast to previous results, the $m=2$ $r$ modes are essentially unaffected by the continuous spectrum and exist even for very relativistic stellar models. We perform our calculations both in the time and frequency domain. In order to numerically solve the infinite system of coupled equations, we truncate it at some value…
We study the evolution of magnetized and rigidly rotating neutron stars within a fully general relativistic implementation of ideal magnetohydrodynamics with no assumed symmetries in three spatial dimensions. The stars are modeled as rotating, magnetized polytropic stars and we examine diverse scenarios to study their dynamics and stability properties. In particular we concentrate on the stability of the stars and possible critical behavior. In addition to their intrinsic physical significance, we use these evolutions as further tests of our implementation which incorporates new developments t…
We investigate the effects ultralight bosonic field dark matter may have on the dynamics of unstable differentially-rotating neutron stars prone to the bar-mode instability. To this aim we perform numerical simulations in general relativity of rotating neutron stars accreting an initial spherically symmetric bosonic field cloud, solving the Einstein-(complex, massive) Klein-Gordon-Euler and the Einstein-(complex) Proca-Euler systems. We find that the presence of the bosonic field can critically modify the development of the bar-mode instability of neutron stars, depending on the total mass of …
In this review article, we present the main results from our most recent research concerning the oscillations of fast rotating neutron stars. We derive a set of time evolution equations for the investigation of non-axisymmetric oscillations of rapidly rotating compact objects in full general relativity, taking into account the contribution of a dynamic spacetime. Using our code, which features high accuracy at comparably low computational expense, we are able to extract the frequencies of non-axisymmetric modes of compact objects with rotation rates up to the Kepler limit. We propose various u…
The 4-parameter exact solution presumably describing the exterior gravitational field of a generic neutron star is presented in a concise explicit form defined by only three potentials. In the equatorial plane, the metric functions of the solution are found to be given by particularly simple expressions that make them very suitable for the use in concrete applications. Following Pappas and Apostolatos, we perform a comparison of the multipole structure of the solution with the multipole moments of the known physically realistic Berti-Stergioulas numerical models of neutron stars to argue that …
We provide details and present additional results on the numerical study of the gravitational-wave emission from the collapse of neutron stars to rotating black holes in three dimensions. More specifically, we concentrate on the advantages and disadvantages of the use of the excision technique and on how alternative approaches to that of excision can be successfully employed. Furthermore, as a first step towards source-characterization, we present a systematic discussion of the influence that rotation and different perturbations have on the waveforms and hence on the energy emitted in gravitat…
The neutrino-antineutrino annihilation into electron-positron pairs near the surface of compact general relativistic stars could play an important role in supernova explosions, neutron star collapse, or for close neutron star binaries near their last stable orbit. General relativistic effects increase the energy deposition rates due to the annihilation process. We investigate the deposition of energy and momentum due to the annihilations of neutrinos and antineutrinos in the equatorial plane of the rapidly rotating neutron and quark stars, respectively. We analyze the influence of general rela…
