| Budget Amount *help |
¥2,100,000 (Direct Cost: ¥2,100,000)
Fiscal Year 1998: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 1997: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 1996: ¥1,000,000 (Direct Cost: ¥1,000,000)
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| Research Abstract |
The aim of this research project was to examine relativisticeffects, which may be in the near future observed in astrophysics. For three years supported by the grant, the following topics are examined.
(1) As the binary of neutron stars shrinks due to gravitationalradiation, the post-Newtonian gravitational effects to the orbital motion and the hydro-dynamical effects become more important. A simplified model, in which the dynamical degrees offreedom are restricted, is adopted to evaluate the spin-orbit, spin-spin and tidal effects in the coalescence.
(2) Quantum mechanical oscillation is calculated for neutrinospropagating in weak external gravitational field. Since the peak of wave packet is important to exhibit the oscillation, the main terms are evaluated. The correction to the result of flat space-time is explicitly derived. The correction should however be careful for the definition of the energy and lengt etc. The interpretation of the correction is subtle since space-times with gravity and without gravity are distinct.
(3)One of well-known approximation used in the Newtonian pulsation theory is so-called the Cowling approximation in which gravitational perturbation is neglected. The accuracy in the relativistic slowly rotating stars is tested. The result shows the accuracy is fairly good without any change of the qualitative pictures.
Axial mode oscillation is also examined in the relativity. At the lowest order of the rotation, the perturbation equation is reduced to singular eigen-value problem. This means that higher order effects are important to determine the spatial function. Indeed, the spatial function describing the oscillation is determined by the Cowling approximation. It is found that the entropy distribution is 'crucial. For the uniform entropy distribution, the mode is restricted to some class.
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