f-Mode instability in relativistic neutron stars

We present the first calculation of the basic properties of the f-mode instability in rapidly rotating relativistic neutron stars, adopting the Cowling approximation. By accounting for dissipation in neutron star matter, i.e., shear or bulk viscosity and superfluid mutual friction, we calculate the associated instability window. For our specific stellar model, a relativistic polytrope, we obtain a minimum gravitational growth time scale (for the dominant ?=m=4 mode) of the order of 10(3)-10(4) s near the Kepler frequency Ω(K) while the instability is active above ～0.92 Ω(K) and for temperatures ～(10(9)-2×10(10)) K, characteristic of newborn neutron stars.     

Neutron stars in relativistic hadron-quark models

Neutron star properties are computed in relativistic models that contain both hadron and quark degrees of freedom. Neutron matter is assumed to have a low-density phase described by quantum hadrodynamics (QHD) and a high-density phase described by quantum chromodynamics (QCD). Several different QHD models and approximations are employed; all use parameters that reproduce the binding energy and density of equilibrium nuclear matter. Calculated neutron star properties depend primarily on the high-density equation of state and cannot be inferred from the symmetry energy or compressibility of equilibrium nuclear matter. If interactions are neglected in the QCD phase, the density of the hadron-quark phase transition is determined by one free parameters, which is the energy/volume needed to create a “bubble” that confines the quarks and gluons. Observed neutron star masses do not constrain this parameter, but stable neutron stars with quark cores can exist only for a limited range of parameter values. When second-order gluon-exchange corrections are included in the QCD phase, these conclusions are unchanged, and the parameter values that lead to stable hadronquark stars are restricted even further.     

Nonlinear r-modes in rapidly rotating relativistic stars

The r-mode instability in rotating relativistic stars has been shown recently to have important astrophysical implications, provided that r-modes are not saturated at low amplitudes by nonlinear effects or by dissipative mechanisms. Here, we present the first study of nonlinear r-modes in isentropic, rapidly rotating relativistic stars, via 3D general-relativistic hydrodynamical evolutions. We find that (1) on dynamical time scales, there is no strong nonlinear coupling of r-modes to other modes at amplitudes of order one-the maximum r-mode amplitude is of order unity. (2) r-modes and inertial modes in isentropic stars are predominantly discrete modes. (3) The kinematical drift associated with r-modes appears to be present in our simulations, but confirmation requires more precise initial data.     

Generic instability of rotating relativistic stars

All rotating perfect fluid configurations having two-parameter equations of state are shown to be dynamically unstable to nonaxisymmetric perturbations in the framework of general relativity. Perturbations of an equilibrium fluid are described by means of a Lagrangian displacement, and an action for the linearized field equations is obtained, in terms of which the symplectic product and canonical energy of the system can be expressed. Previous criteria governing stability were based on the sign of the canonical energy, but this functional fails to be invariant under the gauge freedom associated with a class of trivial Lagrangian displacements, whose existence was first pointed out by Schutz and Sorkin [12]. In order to regain a stability criterion, one must eliminate the trivials, and this is accomplished by restricting consideration to a class of canonical displacements, orthogonal to the trivials with respect to the symplectic product. There nevertheless remain perturbations having angular dependencee ^im ( the azimuthal angle) which, for sufficiently largem, make the canonical energy negative; consequently, even slowly rotating stars are unstable to short wavelength perturbations. To show strict instability, it is necessary to assume that time-dependent nonaxisymmetric perturbations radiate energy to null infinity. As a byproduct of the work, the relativistic generalization of Ertel's theorem (conservation of vorticity in constant entropy surfaces) is obtained and shown to be Noetherrelated to the symmetry associated with the trivial displacements.Supported in part by the National Science Foundation under grant number MPS 74-17456     

General relativistic collapse of rotating stars

Numerical calculations have been made for the formation process of rotating black holes. It is suggested that Kerr black holes may be formed for wide ranges of initial conditions if q (=| total angular momentum |M²) is smaller than unity. For q > 1, an expanding disk or a jet appears.     

On relativistic models of strange stars

The superdense stars with mass-to-size ratio exceeding 0.3 are expected to be made of strange matter. Assuming that the 3-space of the interior space-time of a strange star is that of a three-paraboloid immersed in a four-dimensional Euclidean space, we obtain a two-parameter family of their physically viable relativistic models. This ansatz determines density distribution of the interior self-gravitating matter up to one unknown parameter. The Einstein’s field equations determine the fluid pressure and the remaining geometrical variables. The information about mass-to-size ratio together with the conventional boundary conditions lead to the determination of total mass, radius and other parameters of the stellar configuration.      

Newtonian view of general relativistic stars

The angular ADM reduction of the BTZ spacetime yields a Liouville-type theory. The analysis of the resulting Liouville theory naturally leads to the identification of the stretched horizon. The dynamics associated with the stretched horizon has a feature that seems consistent with the unsmooth horizon; the quantum gravity effects are essential for the unsmoothness. We show that the “anomaly” term in the stress–energy tensor is responsible for the Planck scale energy experienced by an infalling observer.     

Exact regular models for static relativistic stars

We solve the Einstein equations for the case of a static, spherically symmetric distribution of a perfect fluid. We propose a method yielding a broad class of exact solutions. We investigate the question of how to obtaina fortiori regular and equilibrium solutions. We find a new exact solution in a rather simple form and show that it describes a neutron star with mass limit of 0.33 solar masses.The work was done with the financial support of the Krasnoyarsk Regional Science Foundation, grant D(1F0019).Krasnoyarsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 44–48, September, 1994.     

Determining the long living quasi-normal modes of relativistic stars

Methods of finding quasi-normal modes of non-rotating relativistic stars have been well established,however,none of the existing treatments which take spacetime and fluid oscillations fully into account can determine modes of long decay time,e.g.,the p and g mode series,or the f modes for stars with low compactness ratio (M/R). In this paper we show how the quasi-normal modes of long lifetime can be determined through refinements of a treatment originally due to Detweiler and Lindblom. The determination of the p mode series has been argued in the literature to have implication on the life time of gravitational wave sources and stellar stability. In this paper we 1) provide detailed steps in our treatment to facilitate future effort in this direction; 2) correct mistakes in the literature on the formulation; and 3) analyse the accuracy of the quasi-normal mode frequencies obtained and the limitations of the treatment.     

Massive neutron stars and A-hypernuclei in relativistic mean field models

Based on relativistic mean field(RMF) models, we study finite A-hypernuclei and massive neutron stars. The effective N-N interactions PK1 and TM1 are adopted, while the N-A interactions are constrained by reproducing the binding energy of A-hyperon at 1 s orbit of_Λ~(40)Ca. It is found that the A-meson couplings follow a simple relation, indicating a fixed A potential well for symmetric nuclear matter at saturation densities, i.e., around V_Λ=-29.786 MeV. With those interactions, a large mass range of Λ-hypernuclei can be described well. Furthermore,the masses of PSR J1614-2230 and PSR J0348+0432 can be attained adopting the Λ-meson couplings g_(σΛ)/g_(σN)≥0.73,g_(ωΛ)/g_(ωN)≥0.80 for PK1 and g_(σΛ)/g_(σN)≥0.81,g_(ωΛ)/g_(ωN)≥0.90 for TM1, respectively. This resolves the hyperon puzzle without introducing any additional degrees of freedom.     

Structures of rotating traditional neutron stars and hyperon stars in the relativistic $\sigma-\omega$ model

The influence of rotation on the total masses and radii of neutron stars is calculated by Hartles slow-rotation formalism, while the equation of state is considered in a relativistic - model. As the changes of the mass and radius of a real neutron star caused by rotation are very small in comparison with the total mass and radius, one can see that Hartles approximate method is rational to deal with the rotating neutron stars. If three property values, mass, radius and period, are observed for the same neutron star, then the EOS of this neutron star could be decided entirely.Received: 7 November 2003, Revised: 17 February 2004, Published online: 31 August 2004PACS: 04.40.Dg Relativistic stars: structure, stability, and oscillations - 95.30.Sf Relativity and gravitation - 97.10.Kc Stellar rotation - 97.60.Jd Neutron stars     

Visible-laser acceleration of relativistic electrons in a semi-infinite vacuum

We demonstrate a new particle acceleration mechanism using 800 nm laser radiation to accelerate relativistic electrons in a semi-infinite vacuum. The experimental demonstration is the first of its kind and is a proof of principle for the concept of laser-driven particle acceleration in a structure loaded vacuum. We observed up to 30 keV energy modulation over a distance of 1000 lambda, corresponding to a 40 MeV/m peak gradient. The energy modulation was observed to scale linearly with the laser electric field and showed the expected laser-polarization dependence. Furthermore, as expected, laser acceleration occurred only in the presence of a boundary that limited the laser-electron interaction to a finite distance.     

The stability of relativistic stars and the role of the adiabatic index

We study the stability of three analytical solutions of the Einstein’s field equations for spheres of fluid. These solutions are suitable to describe compact objects including white dwarfs, neutron stars and supermassive stars and they have been extensively employed in the literature. We re-examine the range of stability of the Tolman VII solution, we focus on the stability of the Buchdahl solution which is under contradiction in the literature and we examine the stability of the Nariai IV solution. We found that all the mentioned solutions are stable in an extensive range of the compactness parameter. We also concentrate on the effect of the adiabatic index on the instability condition. We found that the critical adiabatic index, depends linearly on the ratio of central pressure over central energy density \(P_c/{\mathcal{E}}_c\), up to high values of the compactness. Finally, we examine the possibility to impose constraints, via the adiabatic index, on realistic equations of state in order to ensure stable configurations of compact objects.     

Analytic modeling of tidal effects in the relativistic inspiral of binary neutron stars

To detect the gravitational-wave (GW) signal from binary neutron stars and extract information about the equation of state of matter at nuclear density, it is necessary to match the signal with a bank of accurate templates. We present the two longest (to date) general-relativistic simulations of equal-mass binary neutron stars with different compactnesses, C=0.12 and C=0.14, and compare them with a tidal extension of the effective-one-body (EOB) model. The typical numerical phasing errors over the ?22 GW cycles are Δ??±0.24 rad. By calibrating only one parameter (representing a higher-order amplification of tidal effects), the EOB model can reproduce, within the numerical error, the two numerical waveforms essentially up to the merger. By contrast, the third post-Newtonian Taylor-T4 approximant with leading-order tidal corrections dephases with respect to the numerical waveforms by several radians.     

Topology of “white stars” in the relativistic fragmentation of light nuclei

Experimental observations of the multifragmentation of relativistic light nuclei by means of emulsions are surveyed. Events that belong to the type of “white stars” and in which the dissociation of relativistic nuclei is not accompanied by the production of mesons and target-nucleus fragments are considered. An almost complete suppression of the binary splitting of nuclei to fragments of charge in excess of two, Z > 2, is a feature peculiar to charge topology in the dissociation of Ne, Mg, Si, and S nuclei. An increase in the degree of nuclear fragmentation manifests itself in the growth of the multiplicity of singly and doubly charged fragments (Z = 1, 2) as the charge of the unexcited fragmenting-nucleus part (which is the main part) decreases. Features of the production of systems formed by extremely light nuclei α, d, and t are studied in the dissociation of the stable isotopes of Li, Be, B, C, N, and O to charged fragments. Manifestations of ³He clustering can be observed in “white stars” in the dissociation of neutron-deficient isotopes of Be, B, C, and N.     

Methods of complex analysis in model calculations of the magnetospheres of relativistic stars

In this paper the two-dimensional problem is solved for the magnetosphere of a relativistic compact star. The direct and reverse currents in the magnetotail are calculated, as well as the force exerted by the magnetic field on the edge of the current layer. The dependence of the solution on the parameters of the model is investigated.     

Equilibrium and stability of relativistic stars in extended theories of gravity

We study static, spherically symmetric equilibrium configurations in extended theories of gravity (ETG) following the notation introduced by Capozziello et al. We calculate the differential equations for the stellar structure in such theories in a very generic form i.e., the Tolman–Oppenheimer–Volkoff generalization for any ETG is introduced. Stability analysis is also investigated with special focus on the particular example of scalar–tensor gravity.