The adiabatic evolution of orbital parameters in the Kerr spacetime

We investigate the adiabatic orbital evolution of a point particle in the Kerr spacetime due to the emission of gravitational waves. In the case that the timescale of the orbital evolution is enough smaller than the typical timescale of orbits, the evolution of orbits is characterized by the change rates of three constants of motion, the energy $E$, the azimuthal angular momentum $L$, and the Carter constant $Q$. For $E$ and $L$, we can evaluate their change rates from the fluxes of the energy and the angular momentum at infinity and on the event horizon according to the balance argument. On the other hand, for the Carter constant, we cannot use the balance argument because we do not know the conserved current associated with it. %and the corresponding conservation law. Recently, Mino proposed a new method of evaluating the averaged change rate of the Carter constant by using the radiative field. In our previous paper we developed a simplified scheme for practical evaluation of the evolution of the Carter constant based on the Mino's proposal. In this paper we describe our scheme in more detail, and derive explicit analytic formulae for the change rates of the energy, the angular momentum and the Carter constant.Comment: 34 pages, no figur

Gauge Problem in the Gravitational Self-Force II. First Post Newtonian Force under Regge-Wheeler Gauge

We discuss the gravitational self-force on a particle in a black hole space-time. For a point particle, the full (bare) self-force diverges. It is known that the metric perturbation induced by a particle can be divided into two parts, the direct part (or the S part) and the tail part (or the R part), in the harmonic gauge, and the regularized self-force is derived from the R part which is regular and satisfies the source-free perturbed Einstein equations. In this paper, we consider a gauge transformation from the harmonic gauge to the Regge-Wheeler gauge in which the full metric perturbation can be calculated, and present a method to derive the regularized self-force for a particle in circular orbit around a Schwarzschild black hole in the Regge-Wheeler gauge. As a first application of this method, we then calculate the self-force to first post-Newtonian order. We find the correction to the total mass of the system due to the presence of the particle is correctly reproduced in the force at the Newtonian order.Comment: Revtex4, 43 pages, no figure. Version to be published in PR

Self-force Regularization in the Schwarzschild Spacetime

We discuss the gravitational self-force on a particle in a black hole space-time. For a point particle, the full (bare) self-force diverges. The metric perturbation induced by a particle can be divided into two parts, the direct part (or the S part) and the tail part (or the R part), in the harmonic gauge, and the regularized self-force is derived from the R part which is regular and satisfies the source-free perturbed Einstein equations. But this formulation is abstract, so when we apply to black hole-particle systems, there are many problems to be overcome in order to derive a concrete self-force. These problems are roughly divided into two parts. They are the problem of regularizing the divergent self-force, i.e., ``subtraction problem'' and the problem of the singularity in gauge transformation, i.e., ``gauge problem''. In this paper, we discuss these problems in the Schwarzschild background and report some recent progress.Comment: 34 pages, 2 figures, submitted to CQG, special volume for Radiation Reaction (CAPRA7

Geometrical locus of massive test particle orbits in the space of physical parameters in Kerr space-time

Gravitational radiation of binary systems can be studied by using the adiabatic approximation in General Relativity. In this approach a small astrophysical object follows a trajectory consisting of a chained series of bounded geodesics (orbits) in the outer region of a Kerr Black Hole, representing the space time created by a bigger object. In our paper we study the entire class of orbits, both of constant radius (spherical orbits), as well as non-null eccentricity orbits, showing a number of properties on the physical parameters and trajectories. The main result is the determination of the geometrical locus of all the orbits in the space of physical parameters in Kerr space-time. This becomes a powerful tool to know if different orbits can be connected by a continuous change of their physical parameters. A discussion on the influence of different values of the angular momentum of the hole is given. Main results have been obtained by analytical methods.Comment: 26 pages, 12 figure

Massive scalar states localized on a de Sitter brane

We consider a brane scenario with a massive scalar field in the five-dimensional bulk. We study the scalar states that are localized on the brane, which is assumed to be de Sitter. These localized scalar modes are massive in general, their effective four-dimensional mass depending on the mass of the five-dimensional scalar field, on the Hubble parameter in the brane and on the coupling between the brane tension and the bulk scalar field. We then introduce a purely four-dimensional approach based on an effective potential for the projection of the scalar field in the brane, and discuss its regime of validity. Finally, we explore the quasi-localized scalar states, which have a non-zero width that quantifies their probability of tunneling from the brane into the bulk.Comment: 14 pages; 5 figure

Braneworld reheating in the bulk inflaton model

In the context of the braneworld inflation driven by a bulk scalar field, we study the energy dissipation from the bulk scalar field into the matter on the brane in order to understand the reheating after inflation. Deriving the late-time behavior of the bulk field with dissipation by using the Green's function method, we give a rigorous justification of the statement that the standard reheating process is reproduced in this bulk inflaton model as long as the Hubble parameter on the brane and the mass of the bulk scalar field are much smaller than the 5-dimensional inverse curvature scale. Our result supports the idea that the brane inflation model caused by a bulk scalar field is expected to be a viable alternative scenario of the early universe.Comment: 5 pages, no figures, final version to be published in PR

Prospects for improving the sensitivity of KAGRA gravitational wave detector

KAGRA is a new gravitational wave detector which aims to begin joint observation with Advanced LIGO and Advanced Virgo from late 2019. Here, we present KAGRA's possible upgrade plans to improve the sensitivity in the decade ahead. Unlike other state-of-the-art detectors, KAGRA requires different investigations for the upgrade since it is the only detector which employs cryogenic cooling of the test mass mirrors. In this paper, investigations on the upgrade plans which can be realized by changing the input laser power, increasing the mirror mass, and injecting frequency dependent squeezed vacuum are presented. We show how each upgrade affects to the detector frequency bands and also discuss impacts on gravitational-wave science. We then propose an effective progression of upgrades based on technical feasibility and scientific scenarios

Brane gravity, higher derivative terms and non-locality

In brane world scenarios with a bulk scalar field between two branes it is known that 4-dimensional Einstein gravity is restored at low energies on either brane. By using a gauge-invariant gravitational and scalar perturbation formalism we extend the theory of weak gravity in the brane world scenarios to higher energies, or shorter distances. We argue that weak gravity on either brane is indistinguishable from 4-dimensional higher derivative gravity, provided that the inter-brane distance (radion) is stabilized, that the background bulk scalar field is changing near the branes and that the background bulk geometry near the branes is warped. This argument holds for a general conformal transformation to a frame in which matter on the branes is minimally coupled to the metric. In particular, Newton's constant and the coefficients of curvature-squared terms in the 4-dimensional effective action are determined up to an ambiguity of adding a Gauss-Bonnet topological term. In other words, we provide the brane-world realization of the so called $R^2$-model without utilizing a quantum theory. We discuss the appearance of composite spin-2 and spin-0 fields in addition to the graviton on the brane and point out a possibility that the spin-0 field may play the role of an effective inflaton to drive brane-world inflation. Finally, we conjecture that the sequence of higher derivative terms is an infinite series and, thus, indicates non-locality in the brane world scenarios.Comment: Latex, 18 pages; a comment on the spurious tensor mode was added; recovery condition of higher derivative gravity clarifie