Akira Tomimatsu

Dimensional reduction in an oscillatory Kaluza-Klein cosmology

We study the dynamical evolution of a seven-dimensional, homogeneous, cosmological model. Anisotropy is prevailed all over the spatial dimensions with the topology S3 × S3, and leads to repetitious (nonchaotic) oscillations of the scale factors. The universe evolves from an initial Kasner phase to a final one, from which the dimensional reduction results. We pay attention to the effect of radiation-energy density and discuss the isotropization of ordinary dimensions through the stabilization of extra dimensions at the Kaluza-Klein radius.

Conditions for Regularity on the Symmetry Axis in a Superposition of Two Kerr-NUT Solutions

A property of the symmetry axis of the metric describing a superposition of two Kerr·NUT solutions is examined. We give some conditions to the parameters included in the metric, in order to assure that the two constituent masses are dynamically balanced by the rotational repulsion against the gravitational attraction, and the total mass becomes positive. It is shown that a suitable choice of the two NUT terms of the constituent solutions is especially important. The space-time structure of single black hole has been extensively studied. However, we have little knowledge about the metric which describes many interacting black holes. Usually, such a metric is dependent on time, and the radiation of gravitational waves cannot be neglected. There exists another possibility that several black holes align along their common rotational axis and take a stationary configuration due to the dynamical balance between the gravixad tational attraction and the rotational repulsion. Recent investigationsi),2) of stationary and axi-symmetric solutions of the vacuum Einstein equation have presented an interesting class of metrics which may represent such an equilibrium configuration. It is obvious that these metrics can be interpreted as a nonlinear superposition of several Kerr-NUT solutions. However, on the symmetry (rotational) axis between the horizons of the Kerr-NUT constituents there may exist any weak singularities of violation of local Euclidean behavior. In order to see whether this superposition is physically acceptable or not, it is necessary to examine the space-time properties on the symmetry axis. The line element of stationary and axi-symmetric vacuum space-time can be written in the form

Distorted rotating black holes

Abstract An axisymmetric stationary metric which describes rotating black holes distorted by surrounding matter is presented by means of the inverse scattering problem technique, and is written down explicitly in terms of the Legendre polynomials. A mass formula for the distorted holes is derived via the Komar integrals over the horizon.

On Gravitational Mass and Angular Momentum of Two Black Holes in Equilibrium

Etude des integrales de Komar pour la metrique decrivant une superposition non lineaire de deux metriques Kerr-NUT. Cette metrique peut etre interpretee comme un systeme de deux trous noirs en equilibre. On definit la masse gravitationnelle et le moment angulaire de chaque trou noir et on observe leffet de leur interaction spin-spin gravitationnelle. On discute de plus du probleme de savoir si les masses gravitationnelles obtenues ici sont positives ou non

Equilibrium of Two Rotating Charged Black Holes and the Dirac String

On etudie le probleme a 2 corps pour des trous noirs charges en rotation en fonction de la solution stationnaire axisymetrique electrovide obtenue a partir de la transformation de Ernst de la famille 2-Kerr-NUT

Condition for Equilibrium of Two Reissner-Nordström Black Holes

On etudie la condition dequilibre de 2 trous noirs de Reissner Nordstrom en fonction de la solution de Cosgrove des equations dEinstein-Maxwell. On trouve que les charges et les masses doivent satisfaire 2 contraintes

Stability of Spherically Symmetric Solutions in Five-Dimensional General Relativity

On etudie la stabilite de solutions a symetrie spherique et independantes du temps en relativite generale a 5 dimensions. On montre que presque toutes les solutions sont instables pour lexcitation de modes monopolaires scalaires

Low-energy behavior of a quantized scalar field in the linearly expanding universe

We study positive frequency mode solutions of a massive scalar field at an initial stage in the spatially flat, linearly expanding Robertson-Walker universe. The essential point is that the initial time is taken to be small enough, but nonzero (e.g., the Planck time), and the mode is determined by a kind of WKB condition. We calculate the created particle spectrum, and show that its low-energy behavior is considerably different from the previous results.

Classical Pseudoparticle Solutions in General Relativity

In order to investigate the physical connection between the quantum tunneling processes (vacuum-to-vacuum transition or thermal radiation) of Yang-Mills and gravitational pseudoxad particles, several properties of the Belavin and Schwarzshild solutions are compared with each other. For this purpose, using Carmelis formalism which describes general relativity in the form of an SL(2, C) gauge field, the Belavin solution is translated into a metric form, and the topological numbers and action (or entropy) are calculated. Moreover, the Schwarzxad shilcl metric is rewritten in the form of a vector potential as a gauge field. Their remarkxad able similarities are shown through such comparisons.

Dynamical Accumulation of an Infinitely Conducting Plasma towards the Neutral Line of a Magnetic Field

Dynamical accumulation process of an infinitely conducting plasma towards the neutral line of a magnetic field is analytically studied within a framework of one-dimensional magnetohydrodynamics. By virtue of a suitable approximation it is shown that after a finite time interval the plasma density and magnetic field are pinched with a characteristic spatial structure near the neutral line, and then release process of the magnetic energy will be set up. These processes in the solar chromosphere are discussed in relation to the Bare phenomena. § I. Introduction In some energetic astrophysical phenomena such as solar flares, X-ray burster and magnetic substorms of the geomagnetic fields, it has been suggested that an explosive release of a magnetic energy may play an important role, and will be caused by accumulation process of the magnetic field above some critical limit. One possible mechanism of such accumulation is a pinch effect of the magnetic field lines to a neutral sheet, at which the magnetic field vanishes. By using the MHD equations, Dungey 1} qualitatively studied a dynamical accumnlation process of the magnetized plasma with an X-type separatorix (a surface made up of field lines bounding the regions of space traversed by the different classes of field lines). He found that (a) the two branches of the separatorix, which initially intersect at almost right angles, approach each other in the direction of plasma flow by the magnetic pressure, (b) in the stage of negligible resistivity (no-disxad sipation of magnetic fields) this process can proceed to form a nearly 1-dimensional structure, and an electric current density (the rotation of B) becomes infinite after a finite time at the neutral line, and (c) the gas pressure cannot prevent the occurrence of this infinity and only the finite resistivity can limit the current density and release the stored magnetic energy. Imshennik and Syrovatskii 2} (herexad after referred to as I-S for abbreviation) investigated the 2-dimensional collapse of the X-type configuration towards a sheet, and found a solution of the non-dissipative and compressible JVIHD equations, which quantitatively shows some parts of the above behaviors (especially (b)). However the analyses of Dungey and I-S are essentially concerned with the time evolution of physical quantities only at the neutral line, and the spatial