The latest binary black hole population estimates argue for a subpopulation of unequal component mass binaries with spins that are likely small but isotropically distributed. This implies a non-zero probability of detecting spin-induced orbital precession and higher order multipole moments in the observed gravitational-wave signals. In this work we directly calculate the probability for precession and higher-order multipoles in each significant gravitational-wave candidate observed by the LIGO--Virgo--KAGRA collaborations (LVK). We find that only one event shows substantial evidence for precession: GW200129_065458, and two events show substantial evidence for higher-order multipoles: GW190412 and GW190814; any evidence for precession and higher-order multipole moments in other gravitational-wave signals is consistent with random fluctuations caused by noise. We then compare our observations with expectations from population models, and confirm that current population estimates from the LVK accurately predict the number of observed events with significant evidence for precession and higher-order multipoles. In particular, we find that this population model predicts that a binary with significant evidence for precession will occur once in every $\sim 50$ detections, and a binary with significant evidence for higher-order multipoles will occur once in every $\sim 70$ observations. However, we emphasise that since substantial evidence for precession and higher-order multipoles have only been observed in three events, any population model that includes a subpopulation of binaries yielding $\sim 2\%$ of events with detectable precession and higher-order multipole moments will likely be consistent with the data.
In this talk relativistic corrections due to Geroch-Hansen multipoles for perihelion precession and node line precession of orbits in a stationary axially symmetric vacuum spacetime endowed with a plane of symmetry will be shown. Patterns of regularity will be discussed.
The LIGO--Virgo--KAGRA collaborations (LVK) produced a catalogue containing gravitational-wave (GW) observations from the first half of the third GW observing run (O3a). This catalogue, GWTC-2.1, includes for the first time a number of \emph{exceptional} GW candidates produced from merging black-hole-binaries with unequivocally unequal component masses. Since subdominant multipole moments and spin-induced orbital precession are more likely to leave measurable imprints on the emitted GW from unequal component mass binaries, these general relativistic phenomena may now be measurable. Indeed, bot…
In $f(R)$ gravity, the metric, presented in the form of the multipole expansion, for the external gravitational field of a spatially compact supported source up to $1/c^3$ order is provided, where $c$ is the velocity of light in vacuum. The metric consists of General Relativity-like part and $f(R)$ part, where the latter is the correction to the former in $f(R)$ gravity. At the leading pole order, the metric can reduce to that for a point-like or ball-like source. For the gyroscope moving around the source without experiencing any torque, the multipole expansions of its spin's angular velociti…
We present a reanalysis of GW151226, the second binary black hole merger discovered by the LIGO--Virgo Collaboration. Previous analysis showed that the best-fit waveform for this event corresponded to the merger of a $\sim 14 \, M_\odot$ black hole with a $\sim 7.5 \, M_\odot$ companion, and the posterior distribution in mass ratio ($q \leq 1$) is rather flat. In this work, we perform parameter estimation using a waveform model that includes the effects of orbital precession and higher-order radiative multipole modes, and we find that the source parameters of GW151226 shift towards the low $q$…
The first terms of the general solution for an asymptotically flat stationary axisymmetric vacuum spacetime endowed with an equatorial symmetry plane are calculated from the corresponding Ernst potential up to seventh order in the radial pseudospherical coordinate. The metric is used to determine the influence of high order multipoles in the perihelion precession of an equatorial orbit and in the node line precession of a non-equatorial orbit with respect to a geodesic circle. Both results are written in terms of invariant quantities such as the Geroch-Hansen multipoles and the energy and angu…
Using the technique of Rindler and Perlick we calculate the total precession per revolution of a gyroscope circumventing the source of Weyl metrics. We establish thereby a link between the multipole moments of the source and an ``observable'' quantity. Special attention deserves the case of the gamma-metric. As an extension of this result we also present the corresponding expressions for some stationary space-times.
We parametrize a large class of corrections to general relativity which include a long-ranged gravitational scalar field as a dynamical degree of freedom in two ways: parametrizing the structure of the correction to the action, and parametrizing the scalar hair (multipole structure) that compact objects and black holes attain. The presence of this scalar hair violates the no-hair theorems present in general relativity, which leads to several important effects. The effects we consider are (i) the interaction between an isolated body and an external scalar field, (ii) the scalar multipole-multip…
A static and axisymmetric solution of the Einstein vacuum equations with a finite number of Relativistic Multipole Moments (RMM) is written in MSA coordinates up to certain order of approximation, and the structure of its metric components is explicitly shown. From the equation of equatorial geodesics we obtain the Binet equation for the orbits and it allows us to determine the gravitational potential that leads to the equivalent classical orbital equations of the perturbed Kepler problem. The relativistic corrections to Keplerian motion are provided by the different contributions of the RMM o…
The electrovacuum around a rotating massive body with electric charge density is described by its multipole moments (mass moments, mass-current moments, electric moments, and magnetic moments). A small uncharged test particle orbiting around such a body moves on geodesics if gravitational radiation is ignored. The waves emitted by the small body carry information about the geometry of the central object, and hence, in principle, we can infer all its multipole moments. Due to its axisymmetry the source is characterized now by four families of scalar multipole moments: its mass moments $M_l$, it…
Black-hole - neutron-star mergers: new numerical-relativity simulations and multipolar effective-one-body model with spin precession and eccentricity
Universitat de les Illes Balears（巴利阿里群岛大学）；Friedrich-Schiller-Universität Jena（耶拿弗里德里希·席勒大学）；The Pennsylvania State University（宾夕法尼亚州立大学）；University of California, Berkeley（加州大学伯克利分校）；Università di Bologna（博洛尼亚大学）
The properties of compact binaries, such as masses and spins, are imprinted in the gravitational-waves they emit and can be measured using parameterised waveform models. Accurately and efficiently describing the complicated precessional dynamics of the various angular momenta of the system in these waveform models is the object of active investigation. One of the key models extensively used in the analysis of LIGO and Virgo data is the single-precessing-spin waveform model IMRPhenomPv2. In this article we present a new model IMRPhenomPv3 which includes the effects of two independent spins in t…
Estimates of the source parameters of gravitational-wave (GW) events produced by compact binary mergers rely on theoretical models for the GW signal. We present the first frequency-domain model for inspiral, merger and ringdown of the GW signal from precessing binary-black-hole systems that also includes multipoles beyond the leading-order quadrupole. Our model, {\tt PhenomPv3HM}, is a combination of the higher-multipole non-precessing model {\tt PhenomHM} and the spin-precessing model {\tt PhenomPv3} that includes two-spin precession via a dynamical rotation of the GW multipoles. We validate …
We derive all second post-Newtonian (2PN), non-precessional effects of spin- orbit coupling on the gravitational wave forms emitted by an inspiraling binary composed of spinning, compact bodies in a quasicircular orbit. Previous post- Newtonian calculations of spin-orbit effects (at 1.5PN order) relied on a fluid description of the spinning bodies. We simplify the calculations by introducing into post-Newtonian theory a delta-function description of the influence of the spins on the bodies' energy-momentum tensor. This description was recently used by Mino, Shibata, and Tanaka (MST) in Teukols…
In the present work, our main objective is to investigate the orbits of spinning test particles around a Schwarzschild black hole under the influence of a quintessence matter field (SQBH). We begin with the dynamics of the spinning test particles around SQBH which is governed by the Mathisson-Papapetrou-Dixon (MPD) equations under the pole-dipole approximation, where the gravitational field and the higher multipoles of the particle are neglected. Depending on the types of saddle points,the effective potential are classified and the possibility of chaotic orbits is discussed. The inner most sta…
Parity Violation in Spin-Precessing Binaries: Gravitational Waves from the Inspiral of Black Holes in Dynamical Chern-Simons Gravity
Illinois Center for Advanced Studies of the Universe, Department of Physics, University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校物理系前沿宇宙学中心）；Dipartimento di Fisica, “Sapienza” Università di Roma & Sezione INFN Roma1（罗马第一大学物理系及INFN罗马第一分部）
We investigate cubic-in-spin effects for inspiralling compact objects binaries, both in the dynamics and the energy flux emitted in gravitational waves, at the leading post-Newtonian order. We use a Lagrangian formalism to implement finite-size effects, and extend it at cubic order in the spins, which corresponds to the octupolar order in a multipolar decomposition. This formalism allows us to derive the equation of motion, equations of precession for the spin, and stress-energy tensor of each body in covariant form, and admits a formal generalization to any multipolar order. For spin-induced …
Core-collapse in massive stars is believed to produce a rapidly spinning black hole surrounded by a compact disk or torus. This forms an energetic MeV-nucleus inside a remnant He-core, powered by black hole-spin energy. The output produces a GRB-supernova, while most of the energy released is in gravitational radiation. The intrinsic gravitational-wave spectrum is determined by multipole mass-moments in the torus. Quadrupole gravitational radiation is radiated at about twice the Keplerian frequency of the torus, which is non-axisymmetric when sufficiently slender, representing a ``{\em black h…
Of all the fundamental parameters of the Sun (diameter, mass, temperature...), the gravitational multipole moments (of degree l and order m) that determine the solar moments of inertia, are still poorly known. However, at the first order (l=2), the quadrupole moment is relevant to many astrophysical applications. It indeed contributes to the relativistic perihelion advance of planets, together with the post-Newtonian (PN) parameters; or to the precession of the orbital plane about the Sun polar axis, the latter being unaffected by the purely relativistic PN contribution. Hence, a precise knowl…
In this work we present 3D numerical relativity simulations of thick accretion disks around tilted Kerr BH. We investigate the evolution of three different initial disk models with a range of initial black hole spin magnitudes and tilt angles. For all the disk-to-black hole mass ratios considered (0.044-0.16) we observe significant black hole precession and nutation during the evolution. This indicates that for such mass ratios, neglecting the self-gravity of the disks by evolving them in a fixed background black hole spacetime is not justified. We find that the two more massive models are uns…
Gravitational waves from the coalescences of black hole and neutron stars afford us the unique opportunity to determine the sources' properties, such as their masses and spins, with unprecedented accuracy. To do so, however, theoretical models of the emitted signal that are i) extremely accurate and ii) computationally highly efficient are necessary. The inclusion of more detailed physics such as higher-order multipoles and relativistic spin-induced orbital precession increases the complexity and hence also computational cost of waveform models, which presents a severe bottleneck to the parame…
We construct an inspiral-merger-ringdown eccentric gravitational-wave (GW) model for binary black holes with non-precessing spins within the effective-one-body formalism. This waveform model, SEOBNRv4EHM, extends the accurate quasi-circular SEOBNRv4HM model to eccentric binaries by including recently computed eccentric corrections up to 2PN order in the gravitational waveform modes, notably the $(l,|m|)=(2,2),(2,1),(3,3),(4,4),(5,5)$ multipoles. The waveform model reproduces the zero eccentricity limit with an accuracy comparable to the underlying quasi-circular model, with the unfaithfulness …
Vector-tensor theories beyond General Relativity have widely been studied in the context of ultraviolet completion of gravity, endowing a mass to the graviton and explaining dark energy phenomena. We here construct rotating black hole solutions in vector-tensor theories valid after the binary neutron star merger event GW170817 that placed very stringent bound on the propagation speed of gravitational waves away from the speed of light. Such valid vector-tensor theories are constructed by performing a generic conformal transformation to Einstein-Maxwell theory, and the new rotating black hole s…
Post-Newtonian inspiral waveform model for eccentric precessing binaries with higher-order modes and matter effects
Max Planck Institute for Gravitational Physics (Albert Einstein Institute)（马克斯·普朗克引力物理研究所（爱因斯坦研究所））；Instituto de Física Teórica UAM/CSIC, Universidad Autónoma de Madrid（马德里自治大学理论物理研究所）；School of Physics and Astronomy and Institute for Gravitational Wave Astronomy, University of Birmingham（伯明翰大学物理与天文学院及引力波天文研究所）；Department of Physics, University of Maryland, College Park（马里兰大学帕克分校物理系）
