Hideyuki Tagoshi

Analytic Black Hole Perturbation Approach to Gravitational Radiation

We review the analytic methods used to perform the post-Newtonian expansion of gravitational waves induced by a particle orbiting a massive, compact body, based on black hole perturbation theory. There exist two different methods of performing the post-Newtonian expansion. Both are based on the Teukolsky equation. In one method, the Teukolsky equation is transformed into a Regge-Wheeler type equation that reduces to the standard Klein Gordon equation in the flat-space limit, while in the other method (which was introduced by Mano, Suzuki, and Takasugi relatively recently, the Teukolsky equation is used directly in its original form. The former’s advantage is that it is intuitively easy to understand how various curved space effects come into play. However, it becomes increasingly complicated when one goes to higher and higher post-Newtonian orders. In contrast, the latter’s advantage is that a systematic calculation to higher post-Newtonian orders can be implemented relatively easily, but otherwise, it is so mathematical that it is hard to understand the interplay of higher order terms. In this paper, we review both methods so that their pros and cons may be seen clearly. We also review some results of calculations of gravitational radiation emitted by a particle orbiting a black hole.

Gravitational field and equations of motion of spinning compact binaries to 2.5 post-Newtonian order

We derive spin-orbit coupling effects on the gravitational field and equations of motion of compact binaries in the 2.5 post-Newtonian approximation to general relativity, one PN order beyond where spin effects first appear. Our method is based on that of Blanchet, Faye, and Ponsot, who use a post-Newtonian metric valid for general (continuous) fluids and represent pointlike compact objects with a

Chapter 1 Black Hole Perturbation

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Present status of large-scale cryogenic gravitational wave telescope

-function stress-energy tensor, regularizing divergent terms by taking the Hadamard finite part. To obtain post-Newtonian spin effects, we use a different

Gravitational Waves by a Particle in Circular Orbits around a Schwarzschild Black Hole 5.5 Post-Newtonian Formula

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Post-Newtonian factorized multipolar waveforms for spinning, non-precessing black-hole binaries

-function stress-energy tensor introduced by Bailey and Israel. In a future paper we will use the 2.5PN equations of motion for spinning bodies to derive the gravitational-wave luminosity and phase evolution of binary inspirals, which will be useful in constructing matched filters for signal analysis. The gravitational field derived here may help in posing initial data for numerical evolutions of binary black hole mergers.

Japanese large-scale interferometers

We present analytic calculations of gravitational waves from a particle orbiting a black hole. We first review the Teukolsky formalism for dealing with the gravitational perturbation of a black hole. Then we develop a systematic method to calculate higher order post-Newtonian corrections to the gravitational waves emitted by an orbiting particle. As applications of this method, we consider orbits that are nearly circular, including exactly circular ones, slightly eccentric ones and slightly inclined orbits off the equatorial plane of a Kerr black hole and give the energy flux and angular momentum flux formulas at infinity with higher order post-Newtonian corrections. Using a different method that makes use of an analytic series representation of the solution of the Teukolsky equation, we also give a post-Newtonian expanded formula for the energy flux absorbed by a Kerr black hole for a circular orbit.

An Efficient Numerical Method for Computing Gravitational Waves Induced by a Particle Moving on Eccentric Inclined Orbits around a Kerr Black Hole

The large-scale cryogenic gravitational wave telescope (LCGT) is the future project of the Japanese gravitational wave group. Two sets of 3 km arm length laser interferometric gravitational wave detectors will be built in a tunnel of Kamioka mine in Japan. LCGT will detect chirp waves from binary neutron star coalescence at 240 Mpc away with a S/N of 10. The expected number of detectable events in a year is two or three. To achieve the required sensitivity, several advanced techniques will be employed such as a low-frequency vibration-isolation system, a suspension point interferometer, cryogenic mirrors, a resonant side band extraction method, a high-power laser system and so on. We hope that the beginning of the project will be in 2005 and the observations will start in 2009.

Current status of the CLIO project

Using the post-Newtonian (PN) expansion technique of the gravitational wave perturbation around a Schwarzschild black hole, we calculate analytically the energy flux of gravitational waves induced by a particle in circular orbits up to the 5.5PN order, i.e.

Black hole ringdown echoes and howls

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