Perturbations of the Kerr black hole in the class of axisymmetric artificial black holes. Abstract Artificial black holes (called also acoustic or optical black holes) are the black holes for the linear wave equaion describing the wave propagation in a moving medium. They attracted a considerable interest of physicists who study them to better understand the black holes in general relativity. W...

Stationary, axisymmetric, vacuum, solutions of Einstein’s equations are obtained as critical points of the total mass among all axisymmetric and (t, φ) symmetric initial data with fixed angular momentum. In this variational principle, the mass is written as a positive definite integral over a spacelike hypersurface. It is also proved that if an absolute minimum exists then it is equal to the ab...

An axisymmetric magnetic field is applied to a spherical, turbulent flow of liquid sodium. An induced magnetic dipole moment is measured which cannot be generated by the interaction of the axisymmetric mean flow with the applied field, indicating the presence of a turbulent electromotive force. It is shown that the induced dipole moment should vanish for any axisymmetric laminar flow. Also obse...

[1] In the paper ‘‘Single-layer axisymmetric model for a Hadley circulation with parameterized eddy momentum forcing’’ by Adam H. Sobel and Tapio Schneider (Journal of Advances in Modeling Earth Systems, 1, 10, doi:10.3894/ JAMES.2009.1.10., 2009) [hereinafter referred to as SS09], we presented an axisymmetric single-layer model for Hadley circulations with parameterized eddy momentum fluxes. R...

We report a new critical solution found at the threshold of axisymmetric gravitational collapse of a complex scalar field with angular momentum. To carry angular momentum the scalar field cannot be axisymmetric; however, its azimuthal dependence is defined so that the resulting stress-energy tensor and spacetime metric are axisymmetric. The critical solution found is nonspherical, discretely se...

In this article we investigate the LBB condition for axisymmetric flow problems. Specifically, the sufficiency condition for approximating pairs to satisfy the LBB condition established by Stenberg in the Cartesian coordinate setting is presented for the cylindrical coordinate setting. For the cylindrical coordinate setting, the Taylor-Hood (k = 2) and conforming Crouzeix-Raviart elements are s...

This short paper describes a numerical model study of an axisymmetric atmospheric circulation (somewhat akin to the Earth’s tropical Hadley circulation) subject to a periodic forcing that cyclically modifies the static stability. The configuration is not particularly realistic as a representation of the true circulation in the Earth’s tropics, but its motivation is justified as an idealized tes...

The Lithium Tokamak eXperiment is a spherical tokamak with a close-fitting low-recycling wall composed of thin lithium layers evaporated onto a stainless steel-lined copper shell. Long-lived non-axisymmetric eddy currents are induced in the shell and vacuum vessel by transient plasma and coil currents and these eddy currents influence both the plasma and the magnetic diagnostic signals that are...

The Global Magnetorotational Instability (MRI) is investigated for a configuration in which the rotation frequency changes only in a narrow transition region. If the vertical wavelength of the unstable mode is of the same order or smaller than the width of this region, the growth rates can differ significantly from those given by a local analysis. In addition, the non-axisymmetric spectrum admi...

Perturbations of the Kerr black hole in the class of axisymmetric artificial black holes. Abstract Artificial black holes (called also acoustic or optical black holes) are the black holes for the linear wave equation describing the wave propagation in a moving medium. They attracted a considerable interest of physicists who study them to better understand the black holes in general relativity. ...