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

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

Geometry and cosmological perturbations in the bulk inflaton model

We consider a braneworld inflation model driven by the dynamics of a scalar field living in the 5-dimensional bulk, the so-called ``bulk inflaton model'', and investigate the geometry in the bulk and large scale cosmological perturbations on the brane. The bulk gravitational effects on the brane are described by a projection of the 5-dimensional Weyl tensor, which we denote by $E_{\mu\nu}$. Focusing on a tachionic potential model, we take a perturbative approach in the anti-de Sitter (AdS$_5$) background with a single de Sitter brane. We first formulate the evolution equations for $E_{\mu\nu}$ in the bulk. Next, applying them to the case of a spatially homogeneous brane, we obtain two different integral expressions for $E_{\mu\nu}$. One of them reduces to the expression obtained previously when evaluated on the brane. The other is a new expression that may be useful for analyzing the bulk geometry. Then we consider superhorizon scale cosmological perturbations and evaluate the bulk effects onto the brane. In the limit $H^2\ell^2\ll1$, where $H$ is the Hubble parameter on the brane and $\ell$ is the bulk curvature radius, we find that the effective theory on the brane is identical to the 4-dimensional Einstein-scalar theory with a simple rescaling of the potential even under the presence of inhomogeneities. % atleast on super-Hubble horizon scales. In particular, it is found that the anticipated non-trivial bulk effect due to the spatially anisotropic part of $E_{\mu\nu}$ may appear only at %second order in the low energy expansion, i.e., at $O(H^4\ell^4)$.Comment: 21 pages including 6 pages for several appendixes, no figure

Stable, Time-Dependent, Exact Solutions for Brane Models with a Bulk Scalar Field

We derive two classes of brane-world solutions arising in the presence of a bulk scalar field. For static field configurations, we adopt a time-dependent, factorizable metric ansatz that allows for radion stabilization. The solutions are characterized by a non-trivial warping along the extra dimension, even in the case of a vanishing bulk cosmological constant, and lead to a variety of inflationary, time-dependent solutions of the 3D scale factor on the brane. We also derive the constraints necessary for the stability of these solutions under time-dependent perturbations of the radion field, and we demonstrate the existence of phenomenologically interesting, stable solutions with a positive cosmological constant on the brane.Comment: 24 pages, latex, 4 eps figur

On Brane World Cosmological Perturbations

We discuss the scalar cosmological perturbations in a 3-brane world with a 5D bulk. We first show explicitly how the effective perturbed Einstein's equations on the brane (involving the Weyl fluid) are encoded into Mukohyama's master equation. We give the relation between Mukohyama's master variable and the perturbations of the Weyl fluid, we also discuss the relation between the former and the perturbations of matter and induced metric on the brane. We show that one can obtain a boundary condition on the brane for the master equation solely expressible in term of the master variable, in the case of a perfect fluid with adiabatic perturbations on a Randall-Sundrum (RS) or Dvali-Gabadadze-Porrati (DGP) brane. This provides an easy way to solve numerically for the evolution of the perturbations as well as should shed light on the various approximations done in the literature to deal with the Weyl degrees of freedom.Comment: 36 pages, 1 figur

Brane Big-Bang Brought by Bulk Bubble

We propose an alternative inflationary universe scenario in the context of Randall-Sundrum braneworld cosmology. In this new scenario the existence of extra-dimension(s) plays an essential role. First, the brane universe is initially in the inflationary phase driven by the effective cosmological constant induced by small mismatch between the vacuum energy in the 5-dimensional bulk and the brane tension. This mismatch arises since the bulk is initially in a false vacuum. Then, the false vacuum decay occurs, nucleating a true vacuum bubble with negative energy inside the bulk. The nucleated bubble expands in the bulk and consequently hits the brane, bringing a hot big-bang brane universe of the Randall-Sundrum type. Here, the termination of the inflationary phase is due to the change of the bulk vacuum energy. The bubble kinetic energy heats up the universe. As a simple realization, we propose a model, in which we assume an interaction between the brane and the bubble. We derive the constraints on the model parameters taking into account the following requirements: solving the flatness problem, no force which prohibits the bubble from colliding with the brane, sufficiently high reheating temperature for the standard nucleosynthesis to work, and the recovery of Newton's law up to 1mm. We find that a fine tuning is needed in order to satisfy the first and the second requirements simultaneously, although, the other constraints are satisfied in a wide range of the model parameters.Comment: 20pages, 5figures, some references added, the previous manuscript has been largely improve

Search for Gravitational Waves Associated with Gamma-Ray Bursts Detected by Fermi and Swift during the LIGO-Virgo Run O3b

We search for gravitational-wave signals associated with gamma-ray bursts (GRBs) detected by the Fermi and Swift satellites during the second half of the third observing run of Advanced LIGO and Advanced Virgo (2019 November 1 15:00 UTC-2020 March 27 17:00 UTC). We conduct two independent searches: A generic gravitational-wave transients search to analyze 86 GRBs and an analysis to target binary mergers with at least one neutron star as short GRB progenitors for 17 events. We find no significant evidence for gravitational-wave signals associated with any of these GRBs. A weighted binomial test of the combined results finds no evidence for subthreshold gravitational-wave signals associated with this GRB ensemble either. We use several source types and signal morphologies during the searches, resulting in lower bounds on the estimated distance to each GRB. Finally, we constrain the population of low-luminosity short GRBs using results from the first to the third observing runs of Advanced LIGO and Advanced Virgo. The resulting population is in accordance with the local binary neutron star merger rate. © 2022. The Author(s). Published by the American Astronomical Society

Narrowband Searches for Continuous and Long-duration Transient Gravitational Waves from Known Pulsars in the LIGO-Virgo Third Observing Run

Isolated neutron stars that are asymmetric with respect to their spin axis are possible sources of detectable continuous gravitational waves. This paper presents a fully coherent search for such signals from eighteen pulsars in data from LIGO and Virgo's third observing run (O3). For known pulsars, efficient and sensitive matched-filter searches can be carried out if one assumes the gravitational radiation is phase-locked to the electromagnetic emission. In the search presented here, we relax this assumption and allow both the frequency and the time derivative of the frequency of the gravitational waves to vary in a small range around those inferred from electromagnetic observations. We find no evidence for continuous gravitational waves, and set upper limits on the strain amplitude for each target. These limits are more constraining for seven of the targets than the spin-down limit defined by ascribing all rotational energy loss to gravitational radiation. In an additional search, we look in O3 data for long-duration (hours-months) transient gravitational waves in the aftermath of pulsar glitches for six targets with a total of nine glitches. We report two marginal outliers from this search, but find no clear evidence for such emission either. The resulting duration-dependent strain upper limits do not surpass indirect energy constraints for any of these targets. © 2022. The Author(s). Published by the American Astronomical Society

Crystallization of Syndiotactic Polystyrene Monitored by Angular Distributions of Polarized Fluorescence

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