Effects of Schwarzschild black hole horizon on isothermal plasma wave dispersion

The 3 + 1 GRMHD equations for Schwarzschild spacetime in Rindler coordinates with isothermal state of plasma are formulated. We consider the cases of non-rotating and rotating backgrounds with non-magnetized and magnetized plasmas. For these cases, the perturbed form of these equations are linearized and Fourier analyzed by introducing plane wave type solutions. The determinant of these equations in each case leads to two dispersion relations which give value of the wave number k. Using the wave number, we obtain information like phase and group velocities etc. which help to discuss the nature of the waves and their characteristics. These provide interesting information about the black hole magnetosphere near the horizon. There are cases of normal and anomalous dispersion. We find a case of normal dispersion of waves when the plasma admits the properties of Veselago medium. Our results agree with those of Mackay et al. according to which rotation of a black hole is required for negative phase velocity propagation.     

Biyouyanagin A, an anti-HIV agent from Hypericum chinense L. var. salicifolium

[structure: see text] A structurally unique hydrophobic compound, biyouyanagin A, was isolated from the MeOH extract of the leaves of Hypericum chinense L. var. salicifolium. The structure of biyouyanagin A was elucidated on the basis of spectroscopic evidence. Biyouyanagin A showed a significant activity against HIV and inhibited cytokine production.     

Electromagnetic plane waves with negative phase velocity in charged black strings

We investigate the propagation regions of electromagnetic plane waves with negative phase velocity in the ergosphere of static charged black strings. For such a propagation, some conditions for negative phase velocity are established that depend on the metric components and the choice of the octant. We conclude that these conditions remain unaffected by the negative values of the cosmological constant.     

Dynamical instability of collapsing radiating fluid

We take the collapsing radiative fluid to investigate the dynamical instability with cylindrical symmetry. We match the interior and exterior cylindrical geometries. Dynamical instability is explored at radiative and non-radiative perturbations. We conclude that the dynamical instability of the collapsing cylinder depends on the critical value γ < 1 for both radiative and nonradiative perturbations.     

Electromagnetic wave propagation with negative phase velocity in regular black holes

We discuss the propagation of electromagnetic plane waves with negative phase velocity in regular black holes. For this purpose, we consider the Bardeen model as a nonlinear magnetic monopole and the Bardeen model coupled to nonlinear electrodynamics with a cosmological constant. It turns out that the region outside the event horizon of each regular black hole does not support negative phase velocity propagation, while its possibility in the region inside the event horizon is discussed.     

Period and index of genus one curves over global fields

The period of a curve is the smallest positive degree of Galois-invariant divisor classes. The index is the smallest positive degree of rational divisors. We construct examples of genus one curves with prescribed period and index over a given global field, as long as the characteristic of the field does not divide the period.     

Charged cylindrical collapse of anisotropic fluid

Following the scheme developed by Misner and Sharp, we discuss the dynamics of gravitational collapse. For this purpose, an interior cylindrically symmetric spacetime is matched to an exterior charged static cylindrically symmetric spacetime using the Darmois matching conditions. Dynamical equations are obtained with matter dissipating in the form of shear viscosity. The effect of charge and dissipative quantities over the cylindrical collapse are studied. Finally, we show that homogeneity in energy density and conformal flatness of spacetime are necessary and sufficient for each other.