Perturbative approach to the structure of rapidly rotating neutron stars

We construct models of rotating stars using the perturbative approach introduced by J. Hartle in 1967, and a set of equations of state proposed to model hadronic interactions in the inner core of neutron stars. We integrate the equations of stellar structure to third order in the angular velocity and show, comparing our results to those obtained with fully non linear codes, to what extent third order corrections are needed to accurately reproduce the moment of inertia of a star which rotates at rates comparable to that of the fastest isolated pulsars.Comment: 17 pages, 5 figures, minor changes to match version accepted by Phys. Rev.

Modeling the iron oxides and oxyhydroxides for the prediction of environmentally sensitive phase transformations

Iron oxides and oxyhydroxides are challenging to model computationally as competing phases may differ in formation energies by only several kJ/mol, they undergo magnetization transitions with temperature, their structures may contain partially occupied sites or long-range ordering of vacancies, and some loose structures require proper description of weak interactions such as hydrogen bonding and dispersive forces. If structures and transformations are to be reliably predicted under different chemical conditions, each of these challenges must be overcome simultaneously, while preserving a high level of numerical accuracy and physical sophistication. Here we present comparative studies of structure, magnetization, and elasticity properties of iron oxides and oxyhydroxides using density functional theory calculations with plane-wave and locally-confined-atomic-orbital basis sets, which are implemented in VASP and SIESTA packages, respectively. We have selected hematite, maghemite, goethite, lepidocrocite, and magnetite as model systems from a total of 13 known iron oxides and oxyhydroxides; and use same convergence criteria and almost equivalent settings in order to make consistent comparisons. Our results show both basis sets can reproduce the energetic stability and magnetic ordering, and are in agreement with experimental observations. There are advantages to choosing one basis set over the other, depending on the intended focus. In our case, we find the method using PW basis set most appropriate, and combine our results to construct the first phase diagram of iron oxides and oxyhydroxides in the space of competing chemical potentials, generated entirely from first principlesComment: 46 pages - Accepted for publication in PRB (19 journal pages), January 201

Frame-like Geometry of Double Field Theory

We relate two formulations of the recently constructed double field theory to a frame-like geometrical formalism developed by Siegel. A self-contained presentation of this formalism is given, including a discussion of the constraints and its solutions, and of the resulting Riemann tensor, Ricci tensor and curvature scalar. This curvature scalar can be used to define an action, and it is shown that this action is equivalent to that of double field theory.Comment: 35 pages, v2: minor corrections, to appear in J. Phys.

Gravitational signals emitted by a point mass orbiting a neutron star: effects of stellar structure

The effects that the structure of a neutron star would have on the gravitational emission of a binary system are studied in a perturbative regime, and in the frequency domain. Assuming that a neutron star is perturbed by a point mass moving on a close, circular orbit, we solve the equations of stellar perturbations in general relativity to evaluate the energy lost by the system in gravitational waves. We compare the energy output obtained for different stellar models with that found by assuming that the perturbed object is a black hole with the same mass, and we discuss the role played by the excitation of the stellar modes. Ouresults indicate that the stellar structure begins to affect the emitted power when the orbital velocity is v >0.2c (about 185 Hz for a binary system composed of two canonical neutron stars). We show that the differences between different stellar models and a black hole are due mainly to the excitation of the quasinormal modes of the star. Finally, we discuss to what extent and up to which distance the perturbative approach can be used to describe the interaction of a star and a pointlike massive body.Comment: 22 pages, 6 figures, to appear in Phys. Rev. D. Revised version, added one table and extended discussio

Perturbing Around A Warped Product Of AdS_4 and Seven-Ellipsoid

We compute the spin-2 Kaluza-Klein modes around a warped product of AdS_4 and a seven-ellipsoid. This background with global G_2 symmetry is related to a U(N) x U(N) N=1 superconformal Chern-Simons matter theory with sixth order superpotential. The mass-squared in AdS_4 is quadratic in G_2 quantum number and KK excitation number. We determine the dimensions of spin-2 operators using the AdS/CFT correspondence. The connection to N=2 theory preserving SU(3) x U(1)_R is also discussed.Comment: 21pp; The second and last paragraphs of section 2, the footnotes 1 and 2 added and to appear in JHE

Reformulating Supersymmetry with a Generalized Dolbeault Operator

The conditions for N=1 supersymmetry in type II supergravity have been previously reformulated in terms of generalized complex geometry. We improve that reformulation so as to completely eliminate the remaining explicit dependence on the metric. Doing so involves a natural generalization of the Dolbeault operator. As an application, we present some general arguments about supersymmetric moduli. In particular, a subset of them are then classified by a certain cohomology. We also argue that the Dolbeault reformulation should make it easier to find existence theorems for the N=1 equations.Comment: 30 pages, no figures. v2: minor correction

Effective actions and N=1 vacuum conditions from SU(3) x SU(3) compactifications

We consider compactifications of type II string theory on general SU(3) x SU(3) structure backgrounds allowing for a very large set of fluxes, possibly nongeometric ones. We study the effective 4d low energy theory which is a gauged N=2 supergravity, and discuss how its data are obtained from the formalism of the generalized geometry on T+T*. In particular we relate Hitchin's special Kaehler metrics on the spaces of even and odd pure spinors to the metric on the supergravity moduli space of internal metric and B-field fluctuations. We derive the N=1 vacuum conditions from this N=2 effective action, as well as from its N=1 truncation. We prove a direct correspondence between these conditions and an integrated version of the pure spinor equations characterizing the N=1 backgrounds at the ten dimensional level.Comment: 54 pages. v2, v3: minor change

Universal law of fractionation for slightly polydisperse systems

By perturbing about a general monodisperse system, we provide a complete description of two-phase equilibria in any system which is slightly polydisperse in some property (e.g., particle size, charge, etc.). We derive a universal law of fractionation which is corroborated by comprehensive experiments on a model colloid-polymer mixture. We furthermore predict that phase separation is an effective method of reducing polydispersity only for systems with a skewed distribution of the polydisperse property

Structure, Deformations and Gravitational Wave Emission of Magnetars

Neutron stars can have, in some phases of their life, extremely strong magnetic fields, up to 10^15-10^16 G. These objects, named magnetars, could be powerful sources of gravitational waves, since their magnetic field could determine large deformations. We discuss the structure of the magnetic field of magnetars, and the deformation induced by this field. Finally, we discuss the perspective of detection of the gravitational waves emitted by these stars.Comment: 11 pages, 2 figures, prepared for 19th International Conference on General Relativity and Gravitation (GR19), Mexico City, Mexico, July 5-9, 201

Two-parameter non-linear spacetime perturbations: gauge transformations and gauge invariance

An implicit fundamental assumption in relativistic perturbation theory is that there exists a parametric family of spacetimes that can be Taylor expanded around a background. The choice of the latter is crucial to obtain a manageable theory, so that it is sometime convenient to construct a perturbative formalism based on two (or more) parameters. The study of perturbations of rotating stars is a good example: in this case one can treat the stationary axisymmetric star using a slow rotation approximation (expansion in the angular velocity Omega), so that the background is spherical. Generic perturbations of the rotating star (say parametrized by lambda) are then built on top of the axisymmetric perturbations in Omega. Clearly, any interesting physics requires non-linear perturbations, as at least terms lambda Omega need to be considered. In this paper we analyse the gauge dependence of non-linear perturbations depending on two parameters, derive explicit higher order gauge transformation rules, and define gauge invariance. The formalism is completely general and can be used in different applications of general relativity or any other spacetime theory.Comment: 22 pages, 3 figures. Minor changes to match the version appeared in Classical and Quantum Gravit