General Relativistic Collapse to Black Holes and Gravitational Waves from Black Holes

One of the important problems in general relativity is to clarify the dynamical nature of space-times. In this article two aspects of dynamical space-times are treated. In Part I general relativistic collapse of axially symmetric rotating stars is discussed. Many numerical results on collapse of rotating massive stars, supermassive stars, deformed stars, stars with magnetic fields and neutron stars are presented. A numerical method for three dimensional problems is also discussed with numerical results on time evolution of pure gravitational waves. In Parts II and III perturbation of black holes is treated. A new formalism, which is suitable when there are perturbation sources such as particles, is given. Many numerical results on gravitational waves induced by a particle or particles orbiting around a spherically symmetric system and an axially symmetric black hole are presented.