Gravitational perturbations of spherically symmetric systems. II. Perfect fluid interiors

Methods developed in a previous paper on perturbations of the Schwarzschild metric are here extended to the treatment of perturbations of perfect fluid stellar models. The perturbations of a perfect fluid sphere are explicitly decomposed into their gauge invariant and gauge dependent parts and a variational principle for the perturbation equations is derived. The Hamiltonian for the perturbations is constructed and a sufficient condition for stability against nonradial, radiative perturbations is derived from it. The stability criterion is applied to two interesting classes of stellar models, polytropic white dwarf models and high-density neutron star cores with pressure proportional to energy density.     

Dynamical Evolution and Leading Order Gravitational Wave Emission of Riemann-S Binaries

An approximate strategy for studying the evolution of binary systems of extended objects is introduced. The stars are assumed to be polytropic ellipsoids. The surfaces of constant density maintain their ellipsoidal shape during the time evolution. The equations of hydrodynamics then reduce to a system of ordinary differential equations for the internal velocities, the principal axes of the stars and the orbital parameters. The equations of motion are given within Lagrangian and Hamiltonian formalism. The special case when both stars are axially symmetric fluid configurations is considered. Leading order gravitational radiation reaction is incorporated, where the quasi-static approximation is applied to the internal degrees of freedom of the stars. The influence of the stellar parameters, in particular the influence of the polytropic index n, on the leading order gravitational waveforms is studied.     

Reissner–Nordström and Charged Gas Spheres

This paper studies polytropic gas spheres with some innovations. The main idea, already advanced in the context of neutral, homogeneous, polytropic stellar models, is to base the theory firmly on a variational principle. Another essential novelty is that the mass distribution extends to infinity, the boundary between bulk and atmosphere being defined by an abrupt change in the polytropic index, triggered by the density. The logical next step is to include the effect of radiation, which is a very significant complication since a full treatment would have to include an account of ionization, thus fields representing electrons, ions, photons, gravitons and neutral atoms as well. In way of preparation, we consider models that are charged but homogeneous, involving only gravity, electromagnetism and a single scalar field that represents both the mass and the electric charge; in short, a non-neutral plasma. While this work only represents a stage in the development of a theory of stars, without direct application to physical systems, it does shed some light on the meaning of the Reissner–Nordström solution of the modified Einstein–Maxwell equations. But the main point of the paper is a suggestion about the proper place of the photon gas in a theory of stellar structure and other plasmas, with an application to a simple system; it is proposed to treat the photon gas as part of the dynamics.     

Polynomial and polytropic approximations in equation of equilibrium post-Newtonian rotating configurations of degenerate neutron gas

This paper considers the polynomial and polytropic approximations in the equation of equilibrium post-Newtonian rotating configurations of a degenerate neutron gas. The concept of a configuration-averaged polytropic index is introduced.     

Dynamical Collapse of White Dwarfs in Hartree- and Hartree-Fock Theory

We study finite-time blow-up for pseudo-relativistic Hartree- and Hartree-Fock equations, which are model equations for the dynamical evolution of white dwarfs. In particular, we prove that radially symmetric initial configurations with negative energy lead to finite-time blow-up of solutions. Furthermore, we derive a mass concentration estimate for radial blow-up solutions. Both results are mathematically rigorous and are in accordance with Chandrasekhar’s physical theory of white dwarfs, stating that stellar configurations beyond a certain limiting mass lead to “gravitational collapse” of these objects. Apart from studying blow-up, we also prove local well-posedness of the initial-value problem for the Hartree- and Hartree-Fock equations underlying our analysis, as well as global-in-time existence of solutions with sufficiently small initial data, corresponding to white dwarfs whose stellar mass is below the Chandrasekhar limit.     

The Milne problem for partially plane-polarized light

An accurate numerical method has been devised to solve half-range problems for the scattering of azimuth-independent polarized radiation in stellar atmospheres. The use of the method is illustrated by solving the Milne problem for the radiation intensity at any optical depth, for the extrapolation distance, and for the law of darkening.     

Linearized Higher-Order Gravity and Stellar Structure

Starting with the general "quadratic gravity" in four dimensions, linearization, assumption of the weak gravitational field to be static and matter to be a perfect fluid, one arrives at the modified Lane-Emden equation. The solutions of the modified Lane-Emden equation are found and the formulas for the stellar radius are obtained in two cases of the polytropic index N = 0 and N = 1. The influence of the additional Yukawa forces in the linearized higher-order gravitation on the Newtonian stellar structure is discussed.     

Thermodynamics of rotating self-gravitating systems

We investigate the statistical equilibrium properties of a system of classical particles interacting via Newtonian gravity, enclosed in a three-dimensional spherical volume. Within a mean-field approximation, we derive an equation for the density profiles maximizing the microcanonical entropy and solve it numerically. At low angular momenta, i.e. for a slowly rotating system, the well-known gravitational collapse “transition” is recovered. At higher angular momenta, instead, rotational symmetry can spontaneously break down giving rise to more complex equilibrium configurations, such as double-clusters (“double stars”). We analyze the thermodynamics of the system and the stability of the different equilibrium configurations against rotational symmetry breaking, and provide the global phase diagram. Received 8 July 2002 Published online 15 October 2002 RID="a" ID="a"e-mail: demartino@hmi.de     

Regular modes in rotating stars

Despite more and more observational data, stellar acoustic oscillation modes are not well understood as soon as rotation cannot be treated perturbatively. In a way similar to semiclassical theory in quantum physics, we use acoustic ray dynamics to build an asymptotic theory for the subset of regular modes which are the easiest to observe and identify. Comparisons with 2D numerical simulations of oscillations in polytropic stars show that both the frequency and amplitude distributions of these modes can accurately be described by an asymptotic theory for almost all rotation rates. The spectra are mainly characterized by two quantum numbers; their extraction from observed spectra should enable one to obtain information about stellar interiors.     

On coherent scattering in stellar atmospheres

An exact solution of the transfer equation for coherent scattering in stellar atmospheres with Planck's function as a sum of elementary functions, is obtained in a simple form with the help of the author's new representation of H-functions of Radiative Transfer.     

Information Erasure and the Generalized Second Law of Black Hole Thermodynamics

We consider the generalized second law of black hole thermodynamics in the light of quantum information theory, in particular information erasure and Landauer’s principle (namely, that erasure of information produces at least the equivalent amount of entropy). A small quantum system outside a black hole in the Hartle-Hawking state is studied, and the quantum system comes into thermal equilibrium with the radiation surrounding the black hole. For this scenario, we present a simple proof of the generalized second law based on quantum relative entropy. We then analyze the corresponding information erasure process, and confirm our proof of the generalized second law by applying Landauer’s principle.     

Hawking Effect with Generalized Uncertainty Principle and Modified Dispersion Relations in de Sitter-Schwarzschild Black Hole

Although the tunneling approach is well established for black hole radiation, much works have been done to support the extension of this approach to more general situations. In this article the Parikh-Kraus-Wilczek tunneling proposal of black hole radiation is considered. The black hole thermodynamics and tunneling radiation are studied, based on both, the generalized uncertainty principle and the modified dispersion relation analysis. It is shown that entropy, temperature and the original Parikh-Kraus-Wilczek tunneling radiation calculation receives new corrections. it has been shown that the results of this two alternative approaches are identical if one uses the suitable expansion coefficients.     

Cosmological Implications of Interacting Polytropic Gas Dark Energy Model in Non-flat Universe

The polytropic gas model is investigated as an interacting dark energy scenario. The cosmological implications of the model including the evolution of EoS parameter w _Λ, energy density Ω_Λ and deceleration parameter q are investigated. We show that, depending on the parameter of model, the interacting polytropic gas can behave as a quintessence or phantom dark energy. In this model, the phantom divide is crossed from below to up. The evolution of q in the context of polytropic gas dark energy model represents the decelerated phase at the early time and accelerated phase later. The singularity of this model is also discussed. Eventually, we establish the correspondence between interacting polytropic gas model with tachyon, K-essence and dilaton scalar fields. The potential and the dynamics of these scalar field models are reconstructed according to the evolution of interacting polytropic gas.     

Generalized uncertainty principle, modified dispersion relation and Reissner-Nordström black hole tunneling radiation

The Parikh-Kraus-Wilczek tunneling proposal of black hole tunneling radiation is considered. Reissner-Nordström black hole thermodynamics is studied according to the generalized uncertainty principle and the modified dispersion relation analysis. It is shown that entropy, temperature and the original Parikh-Kraus-Wilczek calculation of the black hole tunneling probability receive new corrections. The results of these two alternative approaches are identical if one uses the suitable expansion coefficients.     

Dissipative Collapse in the Presence of Λ

We present the general junction conditions for the smooth matching of a spherically symmetric, shear-free spacetime to Vaidya’s outgoing metric across a four-dimensional time-like hypersurface in the presence of a cosmological constant. These results generalise earlier treatments by Santos and co-workers on radiating stellar models. We study the thermal evolution of a particular radiating model within the framework of extended irreversible thermodynamics.     

卫星光通信中恒星背景噪声分析及抑制方法研究

建立了以恒星目视星等、等效温度为参数的恒星辐射谱模型,使利用恒星数据库进行背景噪声分析变得更加简捷。在此基础之上,分析了恒星自身特点及卫星光通信终端参数对背景噪声的抑制能力,提出并定义了抑制参数Ψ,以评价卫星光通信系统的抗噪性能;同时考虑背景噪声光功率对卫星光通信的影响,给出了补偿方法;分析结果表明,通过提高CCD采样频率、降低光学系统带宽等方法,可以有效地减少恒星噪点,降低恒星背景光对卫星光通信系统的影响。该项工作为进一步优化卫星光通信系统参数,提高其空间运行的稳定性打下了基础。