Analytical and Numerical Relativity, and Gravitational Wave Data Analysis
Gravitational Self-Force
One of possible gravitational wave sources for LISA is supermassive black hole-compact object binary systems. Gravitational waves from such systems will allow us to know the space-time structure in the vicinity of the supermassive black hole. Here, in order to extract physical information from gravitational waves, it is necessary not only to prepare precise theoretical waveforms, but also to build up data analysis method. One of our goal is to derive the gravitational reaction force to a compact object orbiting a supermassive black hole, and to construct the precise theoretical templates of gravitational waves that are needed for the gravitational wave astronomy.
Mode-sum regularization
(http://arxiv.org/abs/gr-qc/0111001)
Adiabatic Inspiral
The inspiral waveforms are tractable using black hole perturbation theory in general relativity. In this perturbation theory, the background space-time is the supermassive black hole, and the compact object is treated as a point particle. As a pure theoretical physics interest, it is very interesting to solve the motion of a particle in black hole space-time accurately that is a big probloem in general relativity for several dozen years. As an aside, using the black hole perturbation theory, we can also treat the last stage of black hole merger, called ringdown. The emitted gravitational waves in this ringdown phase carry the information about the mass and spin of the final black hole.
Adiabatic evolution of the Carter constant
(http://arxiv.org/abs/gr-qc/0511151)
Ringdown Data Analysis
The parameter space of the binary systems is very large. This means that we must prepare vast amounts of theoretical waveforms as templates of the gravitational wave data analysis. It is necessary to develop effective and fast analysis methods. By simultaneous online analysis of data from gravitational wave detector, it becomes possible to utilize physical information from electromagnetic wave observation of the binary systems to the full extent. The unity observation of "gravitational and electromagnetic waves" will enter new age. We have developed a search method for gravitational ringing of black holes. The gravitational ringing is due to complex frequency modes called the quasi-normal modes that are excited when a black hole geometry is perturbed. The detection of it will be a direct confirmation of the existence of a black hole. When we use the matched filtering method, the data analysis with a lot of templates required. Here we have to ensure a proper match between the filter as a template and the real wave. It is necessary to keep the detection efficiency as high as possible under limited computational costs.
Template spacing for gravitational ringdown search
(http://arxiv.org/abs/gr-qc/0410037)
Acoustic Black Holes at Low Temperature
We have investigated a condensed matter ``black hole'' analogue, taking the Gross-Pitaevskii (GP) equation as a starting point. The linearized GP equation corresponds to a wave equation on a black hole background, giving quasi-normal modes under some appropriate conditions. We can know the detailed characters and corresponding geometrical information about the acoustic black hole by observing quasi-normal ringdown waves in the low temperature condensed matters. This study is not only an examination of the analogue, but also useful to discuss the data analysis for gravitational ringing.
Gross-Pitaevskii equation
(http://arxiv.org/abs/gr-qc/0411041)
Black Strings
The brane world scenario is a new approach to resolve the problem on how to compactify the higher dimensional spacetime to our 4-dimensional world. One of the remarkable features of this scenario is the higher dimensional effects in classical gravitational interactions at short distances. Due to this feature, there are black string solutions in our 4-dimensional world. Assuming the simplest model of complex minimally coupled scalar field with the local U(1) symmetry, we can show a possibility of black-string formation by merging processes of type I long cosmic strings in our 4-dimensional world. No fine tuning for the parameters in the model might be necessary. The strings will radiate a characteristic gravitational wave.
In 5 dimensional world
(http://arxiv.org/abs/gr-qc/0503058)
Cosmic Strings
Cosmic strings are topological defects produced by U(1) symmetry breaking in the unified field theories, which is believed to occur in the early stage of the universe. Verification of the existence of cosmic strings is a strong evidence of the occurrence of vacuum phase transition in the universe. For detection of the cosmic strings, clarification of the string motion is an important task. We studied stationary rotating Nambu-Goto strings in Minkowski spacetime, and the metric perturbations around them.
Stationary rotating strings
(http://arxiv.org/abs/0811.2846)
Second order perturbations
To derive more precise gravitational waveforms to be used as templates for gravitational wave data analysis, or to extract more information from gravitational waves, second-order calculations are developed in the black hole perturbation theory. The extension of the perturbative calculation to higher order is not only for the self-force calculation, but also to estimate the higher order QNMs, and to formulate the Regge-Wheeler-Zerilli formalism with spin corrections.
Higher perturbative order of QNMs
(http://arxiv.org/abs/0704.3467)
Wave Extraction in Numerical Relativity
In numerical relativity, we usually extract gravitational waves at finite radius, and it is necessary to extrapolate them to infinity. The following formula is derived by assuming the Teukolsky equation in the Schwarzschild spacetime, i.e., the extracted Weyl scalar is evaluated in the Kinnersley tetrad. In (arXiv:1011.4223), the authors noted that this perturbative extrapolation is essential to obtain an excellent phase agreement between the perturbative and characteristic waveforms.
