Neutrino trapping in extremely compact Tolman VII spacetimes

Extremely compact objects trap gravitational waves or neutrinos, assumed to move along null geodesics in the trapping regions. The trapping of neutrinos was extensively studied for spherically symmetric extremely compact objects constructed under the simplest approximation of the uniform energy density distribution, with radius located under the photosphere of the external spacetime; in addition, uniform emissivity distribution of neutrinos was assumed in these studies. Here we extend the studies of the neutrino trapping for the case of the extremely compact Tolman VII objects representing the simplest generalization of the internal Schwarzschild solution with uniform distribution of the energy density, and the correspondingly related distribution of the neutrino emissivity that is thus again proportional to the energy density; radius of such extremely compact objects can overcome the photosphere of the external Schwarzschild spacetime. In dependence on the parameters of the Tolman VII spacetimes, we determine the “local” and “global” coefficients of efficiency of the trapping and demonstrate that the role of the trapping is significantly stronger than in the internal Schwarzschild spacetimes. Our results indicate possible influence of the neutrino trapping in cooling of neutron stars.

Study on Applicability of Large-Area EB Irradiation to Micro-Deburring

In a large-area electron beam (EB) irradiation method developed recently, high energy EB can be obtained without focusing the beam, and large-area EB with almost uniform energy density distribution of 60mm in diameter can be used for instantly melting and evaporating metal surface. Then, the surface smoothing and surface modification of metal molds made of steel, cemented carbide and ceramics can be performed efficiently. When the large-area EB is irradiated to a sharp edge, the material removal remarkably progresses at the edge due to the heat accumulation and EB concentration there, which leads to the edge rounding. Our previous study clarified that micro-deburring was also possible by using this phenomenon. Moreover, this method would be effective for removal of discontinuous micro burrs generated by thermal machining processes, such as EDM and laser cutting. In this study, the possibility to completely remove micro burrs generated in EDM was experimentally investigated. The difference in micro-deburring characteristics with the type of workpiece material was also investigated. As a result, the EDM micro burrs with a height of about up to 50μm could be completely removed by this method. Furthermore, it was made clear that the magnetic property of workpiece materials greatly influenced the deburring characteristics, and the thermal property such as melting point and thermal conductivity also did.

STRING COSMOLOGY WITH MAGNETIC FIELD IN BIANCHI V MODEL

String Cosmology with magnetic field has been studied for Bianchi V space-time model for different directions of the magnetic field and string. For equation of state, we have examined geometric string (Nambu string), Takabayashi string (p-string), string with uniform energy density or barotropic equation of state. Exact analytic solution is possible only in few cases.

On the oscillation spectra of ultra compact stars

Quasi-normal modes of ultra compact stars with uniform energy density have been calculated. For less compact stars, there is only one very slowly damped polar mode (corresponding to the Kelvin f-mode) for each spherical harmonic index l . Further long-lived modes become possible for a sufficiently compact star (roughly when M/R ≥ 1/3). We compare the characteristic frequencies of these resonant polar modes to the axial modes first found by Chandrasekhar & Ferrari ( Proc. R. Soc. Lond . A 434, 449 (1991)). We find that the two spectra approach each other as the star is made more compact. The oscillation frequencies of the corresponding polar and axial modes agree to within a percent for stars more compact than M/R = 0.42. At the same time, the damping times are slightly different. The results illustrate that there is no real difference between the origin of these axial and polar modes: They are essentially spacetime modes.

On the non-radial oscillations of a star. III. A reconsideration of the axial modes

It is shown that for stars with radii in the range 2.25 GM/c 2 < R < ca . 3 GM/c 2 , quasi-normal axial modes of oscillation are possible. These modes are explicitly evaluated for stellar models of uniform energy density.