Perturbative Approach to an orbital evolution around a Supermassive black hole

A charge-free, point particle of infinitesimal mass orbiting a Kerr black hole is known to move along a geodesic. When the particle has a finite mass or charge, it emits radiation which carries away orbital energy and angular momentum, and the orbit deviates from a geodesic. In this paper we assume that the deviation is small and show that the half-advanced minus half-retarded field surprisingly provides the correct radiation reaction force, in a time-averaged sense, and determines the orbit of the particle.Comment: accepted for publication in the Physical Revie

The status of DECIGO

DECIGO (DECi-hertz Interferometer Gravitational wave Observatory) is the planned Japanese space gravitational wave antenna, aiming to detect gravitational waves from astrophysically and cosmologically significant sources mainly between 0.1 Hz and 10 Hz and thus to open a new window for gravitational wave astronomy and for the universe. DECIGO will consists of three drag-free spacecraft arranged in an equilateral triangle with 1000 km arm lengths whose relative displacements are measured by a differential Fabry-Perot interferometer, and four units of triangular Fabry-Perot interferometers are arranged on heliocentric orbit around the sun. DECIGO is vary ambitious mission, we plan to launch DECIGO in era of 2030s after precursor satellite mission, B-DECIGO. B-DECIGO is essentially smaller version of DECIGO: B-DECIGO consists of three spacecraft arranged in an triangle with 100 km arm lengths orbiting 2000 km above the surface of the earth. It is hoped that the launch date will be late 2020s for the present

B_K with the Wilson Quark Action: A Non-Perturbative Resolution of Operator Mixing using Chiral Ward Identities

We propose a non-perturbative method to determine the mixing coefficients of $\Delta s=2$ four-quark operators for the Wilson quark action using chiral Ward identities. The method is applied to calculate B_K in quenched QCD.Comment: 3 pages including 3 figures, Talk presented at LATTICE96(phenomenology) by Y. Kuramash

Radiation reaction and the self-force for a point mass in general relativity

A point particle of mass m moving on a geodesic creates a perturbation h, of the spacetime metric g, that diverges at the particle. Simple expressions are given for the singular m/r part of h and its quadrupole distortion caused by the spacetime. Subtracting these from h leaves a remainder h^R that is C^1. The self-force on the particle from its own gravitational field corrects the worldline at O(m) to be a geodesic of g+h^R. For the case that the particle is a small non-rotating black hole, an approximate solution to the Einstein equations is given with error of O(m^2) as m approaches 0.Comment: 4 pages, RevTe

Tidal Interaction between a Fluid Star and a Kerr Black Hole in Circular Orbit

We present a semi-analytic study of the equilibrium models of close binary systems containing a fluid star (mass $m$ and radius $R_0$) and a Kerr black hole (mass $M$) in circular orbit. We consider the limit $M\gg m$ where spacetime is described by the Kerr metric. The tidally deformed star is approximated by an ellipsoid, and satisfies the polytropic equation of state. The models also include fluid motion in the stellar interior, allowing binary models with nonsynchronized stellar spin (as expected for coalescing neutron star-black hole binaries) to be constructed. Tidal disruption occurs at orbital radius $r_{\rm tide}\sim R_0(M/m)^{1/3}$, but the dimensionless ratio $\hat r_{\rm tide}=r_{\rm tide}/[R_0(M/m)^{1/3}]$ depends on the spin parameter of the black hole as well as on the equation of state and the internal rotation of the star. We find that the general relativistic tidal field disrupts the star at a larger $\hat r_{\rm tide}$ than the Newtonian tide; the difference is particularly prominent if the disruption occurs in the vicinity of the black hole's horizon. In general, $\hat r_{\rm tide}$ is smaller for a (prograde rotating) Kerr black hole than for a Schwarzschild black hole. We apply our results to coalescing black hole-neutron star and black hole-white dwarf binaries. The tidal disruption limit is important for characterizing the expected gravitational wave signals and is relevant for determining the energetics of gamma ray bursts which may result from such disruption.Comment: 29 pages including 8 figures. Minor changes and update. To appear in ApJ, March 20, 2000 (Vol.532, #1

The Transition from Inspiral to Plunge for a Compact Body in a Circular Equatorial Orbit Around a Massive, Spinning Black Hole

There are three regimes of gravitational-radiation-reaction-induced inspiral for a compact body with mass mu, in a circular, equatorial orbit around a Kerr black hole with mass M>>mu: (i) The "adiabatic inspiral regime", in which the body gradually descends through a sequence of circular, geodesic orbits. (ii) A "transition regime", near the innermost stable circular orbit (isco). (iii) The "plunge regime", in which the body travels on a geodesic from slightly below the isco into the hole's horizon. This paper gives an analytic treatment of the transition regime and shows that, with some luck, gravitational waves from the transition might be measurable by the space-based LISA mission.Comment: 8 Pages and 3 Figures; RevTeX; submitted to Physical Review

Rotating black hole orbit functionals in the frequency domain

In many astrophysical problems, it is important to understand the behavior of functions that come from rotating (Kerr) black hole orbits. It can be particularly useful to work with the frequency domain representation of those functions, in order to bring out their harmonic dependence upon the fundamental orbital frequencies of Kerr black holes. Although, as has recently been shown by W. Schmidt, such a frequency domain representation must exist, the coupled nature of a black hole orbit's $r$ and $\theta$ motions makes it difficult to construct such a representation in practice. Combining Schmidt's description with a clever choice of timelike coordinate suggested by Y. Mino, we have developed a simple procedure that sidesteps this difficulty. One first Fourier expands all quantities using Mino's time coordinate $\lambda$. In particular, the observer's time $t$ is decomposed with $\lambda$. The frequency domain description is then built from the $\lambda$-Fourier expansion and the expansion of $t$. We have found this procedure to be quite simple to implement, and to be applicable to a wide class of functionals. We test the procedure using a simple test function, and then apply it in a particularly interesting case, the Weyl curvature scalar $\psi_4$ used in black hole perturbation theory.Comment: 16 pages, 2 figures. Submitted to Phys Rev D. New version gives a vastly improved algorithm due to Drasco for computing the Fourier transforms. Drasco has been added as an author. Also fixed some references and exterminated a small herd of typos; final published versio