Isofrequency pairing of geodesic orbits in Kerr geometry

Abstract ? Bound geodesic orbits around a Kerr black hole can be parametrized by three constants of the motion: the (specific) orbital energy, angular momentum, and Carter constant. Generically, each orbit also has associated with it three frequencies, related to the radial, longitudinal, and (mean) azimuthal motions. Here, we note the curious fact that these two ways of characterizing bound geodesics are not in a one-to-one correspondence. While the former uniquely specifies an orbit up to initial conditions, the latter does not: there is a (strong-field) region of the parameter space in which pairs of physically distinct orbits can have the same three frequencies. In each such isofrequency pair, the two orbits exhibit the same rate of periastron precession and the same rate of Lense-Thirring precession of the orbital plane, and (in a certain sense) they remain “synchronized” in phase.<br/

Gravitational self-force and the effective-one-body formalism between the innermost stable circular orbit and the light ring

We compute the conservative piece of the gravitational self-force (GSF) acting on a particle of mass m_1 as it moves along an (unstable) circular geodesic orbit between the innermost stable circular orbit (ISCO) and the light ring of a Schwarzschild black hole of mass m_2>> m_1. More precisely, we construct the function h_{uu}(x) = h_{\mu\nu} u^{\mu} u^{\nu} (related to Detweiler's gauge-invariant "redshift" variable), where h_{\mu\nu} is the regularized metric perturbation in the Lorenz gauge, u^{\mu} is the four-velocity of m_1, and x= [Gc^{-3}(m_1+m_2)\Omega]^{2/3} is an invariant coordinate constructed from the orbital frequency \Omega. In particular, we explore the behavior of h_{uu} just outside the "light ring" at x=1/3, where the circular orbit becomes null. Using the recently discovered link between h_{uu} and the piece a(u), linear in the symmetric mass ratio \nu, of the main radial potential A(u,\nu) of the Effective One Body (EOB) formalism, we compute a(u) over the entire domain 0<u<1/3. We find that a(u) diverges at the light-ring as ~0.25 (1-3u)^{-1/2}, explain the physical origin of this divergence, and discuss its consequences for the EOB formalism. We construct accurate global analytic fits for a(u), valid on the entire domain 0<u<1/3 (and possibly beyond), and give accurate numerical estimates of the values of a(u) and its first 3 derivatives at the ISCO, as well as the O(\nu) shift in the ISCO frequency. In previous work we used GSF data on slightly eccentric orbits to compute a certain linear combination of a(u) and its first two derivatives, involving also the O(\nu) piece \bar d(u) of a second EOB radial potential {\bar D}(u,\nu). Combining these results with our present global analytic representation of a(u), we numerically compute {\bar d}(u)$ on the interval 0<u\leq 1/6.Comment: 44 pages, 8 figures. Extended discussion in Section V and minor typographical corrections throughout. Version to be published in PR

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

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

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

Quantum fluctuations in brane-world inflation without inflaton on the brane

A Randall-Sundrum type brane-cosmological model in which slow-roll inflation on the brane is driven solely by a bulk scalar field was recently proposed by Himemoto and Sasaki. We analyze their model in detail and calculate the quantum fluctuations of the bulk scalar field $\phi$ with $m^2=V''(\phi)$. We decompose the bulk scalar field into the infinite mass spectrum of 4-dimensional fields; the field with the smallest mass-square, called the zero-mode, and the Kaluza-Klein modes above it with a mass gap. We find the zero-mode dominance of the classical solution holds if $|m^2|\bar\ell^2\ll1$, where $\bar{\ell}$ is the curvature radius of the effectively anti-de Sitter bulk, but it is violated if $|m^2|\bar\ell^2\gg1$, though the violation is very small. Then we evaluate the vacuum expectation value $$ on the brane. We find the zero-mode contribution completely dominates if $|m^2|\bar{\ell}^2\ll 1$ similar to the case of classical background. In contrast, we find the Kaluza-Klein contribution is small but non-negligible if the value of $|m^2|\bar{\ell}^2$ is large.Comment: 12pages, 1 figure, typos corrected, a couple of paragraphs modified but no major change in the text, 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

Exactly solvable model for cosmological perturbations in dilatonic brane worlds

We construct a model where cosmological perturbations are analytically solved based on dilatonic brane worlds. A bulk scalar field has an exponential potential in the bulk and an exponential coupling to the brane tension. The bulk scalar field yields a power-law inflation on the brane. The exact background metric can be found including the back-reaction of the scalar field. Then exact solutions for cosmological perturbations which properly satisfy the junction conditions on the brane are derived. These solutions provide us an interesting model to understand the connection between the behavior of cosmological perturbations on the brane and the geometry of the bulk. Using these solutions, the behavior of an anisotropic stress induced on the inflationary brane by bulk gravitational fields is investigated.Comment: 30 pages, typos corrected, reference adde

Effects of paternal high-fat diet and maternal rearing environment on the gut microbiota and behavior.

Exposing a male rat to an obesogenic high-fat diet (HFD) influences attractiveness to potential female mates, the subsequent interaction of female mates with infant offspring, and the development of stress-related behavioral and neural responses in offspring. To examine the stomach and fecal microbiome\u27s potential roles, fecal samples from 44 offspring and stomach samples from offspring and their fathers were collected and bacterial community composition was studied by 16 small subunit ribosomal RNA (16S rRNA) gene sequencing. Paternal diet (control, high-fat), maternal housing conditions (standard or semi-naturalistic housing), and maternal care (quality of nursing and other maternal behaviors) affected the within-subjects alpha-diversity of the offspring stomach and fecal microbiomes. We provide evidence from beta-diversity analyses that paternal diet and maternal behavior induced community-wide shifts to the adult offspring gut microbiome. Additionally, we show that paternal HFD significantly altered the adult offspring Firmicutes to Bacteroidetes ratio, an indicator of obesogenic potential in the gut microbiome. Additional machine-learning analyses indicated that microbial species driving these differences converged on Bifidobacterium pseudolongum. These results suggest that differences in early-life care induced by paternal diet and maternal care significantly influence the microbiota composition of offspring through the microbiota-gut-brain axis, having implications for adult stress reactivity