Waves in general relativistic two-fluid plasma around a Schwarzschild black hole

Waves propagating in the relativistic electron-positron or ions plasma are investigated in a frame of two-fluid equations using the 3+1 formalism of general relativity developed by Thorne, Price and Macdonald (TPM). The plasma is assumed to be freefalling in the radial direction toward the event horizon due to the strong gravitational field of a Schwarzschild black hole. The local dispersion relations for transverse and longitudinal waves have been derived, in analogy with the special relativistic formulation as explained in an earlier paper, to take account of relativistic effects due to the event horizon using WKB approximation.     

An analysis of wave properties of isothermal plasma around Reissner-Nordström black hole

The 3+1 spacetime split is used in a preliminary investigation of waves propagating in a medium of isothermal plasma in the vicinity of event horizon of Reissner-Nordström planar analogue. The general relativistic magnetohydrodynamic equations for isothermal have been investigated there. The dispersion relations are obtained by using linear perturbation and Fourier analyze techniques for non-rotating and rotating, non-magnetized and magnetized environment. The wave number, phase velocity, group velocity etc. are shown to discuss the nature of the waves.     

Formation of vortices in the presence of sheared electron flows in the earth's ionosphere

It is shown that sheared electron flows can generate long as well as short wavelength (in comparison with the ion gyroradius) electrostatic waves in a nonuniform magnetplasma. For this purpose, we derive dispersion relations by employing two-fluid and hybrid models; in the two-fluid model the dynamics of both the electrons and ions are governed by the hydrodynamic equations and the guiding center fluid drifts, whereas the hybrid model assumes kinetic ions and fluid electrons. Explicit expressions for the growth rates and thresholds are presented. Linearly excited waves attain finite amplitudes and start interacting among themselves. The interaction is governed by the nonlinear equations containing the Jacobian nonlinearities. Stationary solutions of the nonlinear mode coupling equations can be represented in the form of a dipolar vortex and a vortex street. Conditions under which the latter arise are given. Numerical results for the growth rates of linearly excited modes as well as for various types of vortices are displayed for the parameters that are relevant for the F-region of the Earth's ionosphere. It is suggested that the results of the present investigation are useful in understanding the properties of nonthermal electrostatic waves and associated nonlinear vortex structures in the Earth's ionosphere.     

Black hole spin dependence of general relativistic multi-transonic accretion close to the horizon

We introduce a novel formalism to investigate the role of the spin angular momentum of astrophysical black holes in influencing the behavior of low angular momentum general relativistic accretion. We propose a metric independent analysis of axisymmetric general relativistic flow, and consequently formulate the space and time dependent equations describing the general relativistic hydrodynamic accretion flow in the Kerr metric. The associated stationary critical solutions for such flow equations are provided and the stability of the stationary transonic configuration is examined using an elegant linear perturbation technique. We examine the properties of infalling material for both prograde and retrograde accretion as a function of the Kerr parameter at extremely close proximity to the event horizon. Our formalism can be used to identify a new spectral signature of black hole spin, and has the potential of performing the black hole shadow imaging corresponding to the low angular momentum accretion flow.     

On some transonic aspects of general relativistic spherical accretion on to Schwarzschild black holes

The equations governing general relativistic, spherically symmetric, hydrodynamic accretion of polytropic fluid on to black holes are solved in the Schwarzschild metric to investigate some of the transonic properties of the flow. Only stationary solutions are discussed. For such accretion, it has been shown that real physical sonic points may form even for flow with   γ <4/3  or   γ >5/3  . The behaviour of some flow variables in the close vicinity of the event horizon is studied as a function of specific energy and the polytropic index of the flow.     

Reflection Properties of Gravito-MHD Waves in an Inhomogeneous Horizontal Magnetic Field

We derive the dispersion equation for gravito-magnetohydrodynamical (MHD) waves in an isothermal, gravitationally stratified plasma with a horizontal inhomogeneous magnetic field. Sound and Alfvén speeds are constant. Under these conditions, it is possible to derive analytically the equations for gravito-MHD waves. The high values of the viscous and magnetic Reynolds numbers in the solar atmosphere imply that the dissipative terms in the MHD equations are negligible, except in layers around the positions where the frequency of the MHD wave equals the local Alfvén or slow wave frequency. Outside these layers the MHD waves are accurately described by the equations of ideal MHD. We consider waves that propagate energy upward in the atmosphere. For the plane boundary, z=0, between two isothermal plasma regions with horizontal but different magnetic fields, we discuss the boundary conditions and derive the equations for the reflection and transmission coefficients. In the simpler case of a gravitationally stratified plasma without magnetic field, these coefficients describe the reflection and transmission properties of gravito-acoustic waves.     

Entropy of viscous Universe models

The cosmological event horizon entropy and the apparent horizon entropy of the ΛCDM and the Bianchi type I Universe model with viscosity has been calculated numerically, and analytically in the large time limit. It is shown that for these Universe models the cosmological event horizon entropy increases with time and for large times it approaches a finite maximum value. The effect of viscosity upon the entropy is also studied and we have found that its role is to decrease the entropy. The bigger the viscosity coefficient is the less the entropy will be. Furthermore, the radiation entropy for the ΛCDM Universe model with and without viscosity is investigated, and together with the cosmological event horizon entropy are used to examine the validity of the generalized second law of thermodynamics, which states that the total rate of change of entropy of the Universe is never negative, in this Universe model.     

Effects of cosmic rays and density inhomogeneity of the circumstellar medium on the formation of a supernova shell

We consider the self-similar problem of a supernova explosion in a radially inhomogeneous medium by taking into account the generation of accelerated relativistic particles. The initial density of the medium is assumed to decrease with distance from the explosion center as a power law, ρ ₀ = A/r ^θ. We use a two-fluid approach in which the total pressure in the medium is the sum of the circumstellar gas pressure and the relativistic particle pressure. The relativistic particle pressure at the shock front is specified as an external parameter. This approach is applicable in the case where the diffusion coefficient of accelerated particles is small and the thickness of the shock front is much smaller than its radius. We have numerically solved a system of ordinary differential equations for the dimensionless quantities that describe the velocity and density behind the shock front as well as the nonrelativistic gas and relativistic particle pressures for various parameters of the inhomogeneity of the medium and various compression ratios of the medium at the shock front. We have established that the shock acceleration of cosmic rays affects most strongly the formation of a supernova shell (making it thinner) in a homogeneous circumstellar medium. A decrease in the circumstellar matter density with distance from the explosion center causes the effect of shock-accelerated relativistic particles on the supernova shell formation to weaken considerably. Inhomogeneity of the medium makes the shell thicker and less dense, while an increase in the compression ratio of the medium at the shock front causes the shell to become thinner and denser. As the relativistic particle density increases, the effect of circumstellar matter inhomogeneity on the shell formation becomes weaker.     

Torsional oscillations of magnetized relativistic stars

Strong magnetic fields in relativistic stars can be a cause of crust fracturing, resulting in the excitation of global torsional oscillations. Such oscillations could become observable in gravitational waves or in high-energy radiation, thus becoming a tool for probing the equation of state of relativistic stars. As the eigenfrequency of torsional oscillation modes is affected by the presence of a strong magnetic field, we study torsional modes in magnetized relativistic stars. We derive the linearized perturbation equations that govern torsional oscillations coupled to the oscillations of a magnetic field, when variations in the metric are neglected (Cowling approximation). The oscillations are described by a single two-dimensional wave equation, which can be solved as a boundary-value problem to obtain eigenfrequencies. We find that, in the non-magnetized case, typical oscillation periods of the fundamental     torsional modes can be nearly a factor of 2 larger for relativistic stars than previously computed in the Newtonian limit. For magnetized stars, we show that the influence of the magnetic field is highly dependent on the assumed magnetic field configuration, and simple estimates obtained previously in the literature cannot be used for identifying normal modes observationally.     

Ion-acoustic solitary waves in a fully relativistic ion-electron-positron plasma

A fully and coherent relativistic fluid model derived from the covariant formulation of relativistic fluid equations is used to study ion-acoustic solitary waves in a fully relativistic ion-electron-positron plasma. This approach has the characteristic to be consistent with the relativistic principle and consequently leads to a more general set of equations valid for fully relativistic plasmas with arbitrary Lorentz relativistic factor. Our results may be relevant to cosmic relativistic double- layers and relativistic plasma structures involving energetic plasma flows that may occur in space plasmas. Furthermore, they may complement and provide new insights into recently published results (G. Lu et al. in Astrophys. Space Sci., doi:, 2010).     

Linear perturbations in a universe with a cosmological constant

There is now evidence that the cosmological constant Λ has a non-zero positive value. Alternative scenarios to a pure cosmological constant model are provided by quintessence, an effective negative pressure fluid permeating the Universe. Recent results indicate that the energy density ρ and the pressure p of this fluid are constrained by − ρ ≤ p ≲−0.6 ρ . As p =− ρ is equivalent to the pure cosmological constant model, it is appropriate to analyse this particular, but important, case further.
We study the linear theory of perturbations in a Friedmann–Robertson–Walker universe with a cosmological constant. We obtain the equations for the evolution of the perturbations in the fully relativistic case, for which we analyse the single-fluid and two-fluid cases. We obtain solutions to these equations in appropriate limits. We also study the Newtonian approximation. We find that for a positive cosmological constant universe (i) the perturbations will grow more slowly in the relativistic regime for a two-fluid composed of dark matter and radiation, and (ii) in the Newtonian regime the perturbations stop growing.     

Why Newtonian gravity is reliable in large-scale cosmological simulations

Until now, it has been common to use Newtonian gravity to study the non-linear clustering properties of large-scale structures. Without confirmation from Einstein's theory, however, it has been unclear whether we can rely on the analysis (e.g. near the horizon scale). In this work we will provide confirmation of the use of Newtonian gravity in cosmology, based on the relativistic analysis of weakly non-linear situations to third order in perturbations. We will show that, except for the gravitational-wave contribution, the relativistic zero-pressure fluid equations perturbed to second order in a flat Friedmann background coincide exactly with the Newtonian results. We will also present the pure relativistic correction terms appearing in the third order. The third-order correction terms show that these terms are the linear-order curvature perturbation times the second-order relativistic/Newtonian terms. Thus, the pure general relativistic corrections in the third order are independent of the horizon scale and are small when considering the large-scale structure of the Universe because of the low-level temperature anisotropy of the cosmic microwave background radiation. Since we include the cosmological constant, our results are relevant to currently favoured cosmology. As we prove that the Newtonian hydrodynamic equations are valid in all cosmological scales to second order, and that the third-order correction terms are small, our result has the important practical implication that one can now use the large-scale Newtonian numerical simulation more reliably as the simulation scale approaches and even goes beyond the horizon. In a complementary situation, where the system is weakly relativistic (i.e. far inside the horizon) but fully non-linear, we can employ the post-Newtonian approximation. We also show that in large-scale structures, the post-Newtonian effects are quite small.     

Cosmic-Ray Momentum Diffusion in Magnetosonic versus Alfvénic Turbulent Field

Energetic particle transport in a finite amplitude magnetosonic and Alfvénic turbulence is considered using the Monte Carlo particle simulations, which involve integration of particle equations of motion. We show that in the low- plasma the cosmic-ray acceleration can be the most important damping process for magnetosonic waves. Assuming such conditions we derive the momentum diffusion coefficient Dp, for relativistic particles in the presence of anisotropic finite-amplitude turbulent wave fields, for flat and Kolmogorov-type turbulence spectra, respectively. We confirm the possibility of larger values of Dp occurring due to transit-time damping resonance interaction in the presence of isotropic fast-mode waves in comparison to the Alfvén waves of the same amplitude (cf. Schlickeiser and Miller, 1997). The importance of quasi-perpendicular fast-mode waves is stressed for the acceleration of high velocity particles.     

Cold plasma wave analysis in magneto-rotational fluids

This paper is devoted to investigate the cold plasma wave properties. The analysis has been restricted to the neighborhood of the pair production region of the Kerr magnetosphere. The Fourier analyzed general relativistic magnetohydrodynamical equations are dealt under special circumstances and dispersion relations are obtained. We find the x-component of the complex wave vector numerically. The corresponding components of the propagation vector, attenuation vector, phase and group velocities are shown in graphs. The direction and dispersion of waves are investigated.     

Equations of general relativistic radiation hydrodynamics from a tensor formalism

Radiation interacts with matter via exchange of energy and momentum. When matter is moving with a relativistic velocity or when the background space–time is strongly curved, rigorous relativistic treatment of hydrodynamics and radiative transfer is required. Here, we derive fully general relativistic radiation hydrodynamic equations from a covariant tensor formalism. The equations can be applied to any three-dimensional problems and are rather straightforward to understand compared to the comoving frame-based equations. The current approach is applicable to any space–time or coordinates, but in this work we specifically choose the Schwarzschild space–time to show explicitly how the hydrodynamic and the radiation moment equations are derived. Some important aspects of relativistic radiation hydrodynamics and the difficulty with the radiation moment formalism are discussed as well.     

Finite-β effects on the radiative thermal instability in magnetized plasmas

The radiative thermal instability is investigated taking into account finite-, or electromagnetic, effects. The two-fluid model for magnetized plasmas together with the Maxwell equations are used to derive a general dispersion relation valid for compressional perturbations with frequency below the electron-cyclotron frequency. The growth rates of the radiative thermal instabilities involving fast magnetosonic flute-like and low-frequency hydromagnetic perturbations are presented.     

Electrostatic envelope excitations under transverse perturbations in a plasma with nonextensive hot electrons

Nonlinear dynamics of electron acoustic waves (EAWs) in a plasma consisting of stationary ions, cool inertial electrons and hot electrons having a nonextensive distribution is studied. Under transverse perturbations, the nonlinear wave can be described by the general form of the Davey-Stewartson (DS) equations. The reductive perturbation technique is employed to derive Davey-Stewartson equations. From the solutions of these equations, amplitude modulation properties and stability regions of EAWs are studied in two-dimensional plasma. Further, the influence of nonextensivity of hot electrons (via q) on the characteristics of EAWs has been analysed.     

Modulational instability of nonlinear waves in the relativistic plasma with account of the nonlinear Landau damping

The modulational instability of the weakly nonlinear longitudinal Langmuir as well as the transverse electromagnetic waves, propagation in the relativistic plasma without the static fields is described. The nonlinear Schrödinger equation taking account of the nonlinear Landau damping for these waves has been derived by means of the relativistic Vlasov and Maxwell equations. The plasma with the weakly relativistic temperature and that with an ultrarelativistic one has been investigated. In the first case, for the electron-proton plasma with the temperature more than 2.3 KeV we found the regional change of the wave numbers for which the soliton of two types, subsonic and supersonic, can exist. The soliton of the transverse waves can exist when the group velocity of the waves is between the thermal velocity of the electron and ion and the length of the linear waves is less than 2c/ _pi .In the second case the regions of the wave numbers, with the solitons of the Langmuir and transverse waves have been determined.The nonlinear waves in the electron-positron plasma and the waves with the phase velocity, which is about the light one, are also considered in the following paper.