We present a study of the gravitational waveforms from a series of spinning, equal-mass black hole binaries focusing on the harmonic content of the waves and the contribution of the individual harmonics to the signal-to-noise ratio. The gravitational waves were produced from two series of evolutions with black holes of initial spins equal in magnitude and anti-aligned with each other. In one series the magnitude of the spin is varied; while in the second, the initial angle between the black-hole spins and the orbital angular momentum varies. We also conduct a preliminary investigation into using these waveforms as templates for detecting spinning binary black holes. Since these runs are relativity short, containing about two to three orbits, merger and ringdown, we limit our study to systems of total mass greater than 50 solar masses. This choice ensures that our waveforms are present in the ground-based detector band without needing addition gravitational wave cycles. We find that while the mode contribution to the signal-to-noise ratio varies with the initial angle, the total mass of the system caused greater variations in the match.
We analyze a new numerical relativity dataset of spinning but nonprecessing binary black holes on eccentric orbits, with eccentricities from approximately $0.1$ to $0.5$, with dimensionless spins up to $0.75$ included at mass ratios $q=m_1/m_2 = (1, 2)$, and further nonspinning binaries at mass ratios $q = (1.5, 3, 4)$. A comparison of the final mass and spin of these simulations with noneccentric data extends previous results in the literature on circularization of eccentric binaries to the spinning case. For the $(l,m)=(2,2)$ spin-weighted spherical harmonic mode we construct eccentric hybri…
We use the open source, community-driven, numerical relativity software, the Einstein Toolkit to study the physics of eccentric, spinning, nonprecessing binary black hole mergers with mass-ratios $q=\{2, 4, 6\}$, individual dimensionless spin parameters $χ_{1z}=\pm0.6$, $χ_{2z}=\pm0.3$, that include higher order gravitational wave modes $\ell\leq4$, except for memory modes. Assuming stellar mass binary black hole mergers that may be detectable by the advanced LIGO detectors, we find that including modes up to $\ell=4$ increases the signal-to-noise of compact binaries between $3.5\%$ to $35\%$,…
We present a reduced-order surrogate model of gravitational waveforms from non-spinning binary black hole systems with comparable to large mass-ratio configurations. This surrogate model, \texttt{BHPTNRSur1dq1e4}, is trained on waveform data generated by point-particle black hole perturbation theory (ppBHPT) with mass ratios varying from 2.5 to 10,000. \texttt{BHPTNRSur1dq1e4} extends an earlier waveform model, \texttt{EMRISur1dq1e4}, by using an updated transition-to-plunge model, covering longer durations up to 30,500 $m_1$ (where $m_1$ is the mass of the primary black hole), includes severa…
We investigate the possibility of testing short distance modifications to General Relativity via higher curvature terms in the fundamental gravity Lagrangian by analysing their impact on observations of spinning astronomical binary systems. By using effective field theory methods applied to the 2-body problem, generic lower bounds on the short-distance scale accompanying high curvature terms can be set. In particular we extend known results by deriving spin-dependent effects in binding energy, radiation emission process, and spin precession equations in binary systems, which are the fundamenta…
Spinning Black Holes in Modified Gravity via Spectral Methods
Illinois Center for Advanced Studies of the Universe & Department of Physics, University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校高级宇宙学中心及物理系）；DAMTP, Centre for Mathematical Sciences, University of Cambridge（剑桥大学数学科学中心应用数学与理论物理系）
Measurements of black-hole spins are of crucial importance to fulfill the promise of gravitational-wave astronomy. On the astrophysics side, spins are perhaps the cleanest indicator of black-hole evolutionary processes, thus providing a preferred way to discriminate how LIGO's black holes form. On the relativity side, spins are responsible for peculiar dynamical phenomena (from precessional modulations in the long inspiral to gravitational-wave recoils at merger) which encode precious information on the underlying astrophysical processes. I present some examples to explore this deep and fascin…
In this work we study the dynamics of spinning binary black hole systems in the strong field regime. For this purpose we extract from numerical relativity simulations the binding energy, specific orbital angular momentum, and gauge-invariant orbital frequency. The goal of our work is threefold: First, we extract the individual spin contributions to the binding energy, in particular the spin-orbit, spin-spin, and cubic-in-spin terms. Second, we compare our results with predictions from waveform models and find that while post-Newtonian approximants are not capable of representing the dynamics d…
This paper presents general relativistic numerical simulations of uniformly rotating polytropes. Equations are developed using MSQI coordinates, but taking a logarithm of the radial coordinate. The result is relatively simple elliptical differential equations. Due to the logarithmic scale, we can resolve solutions with near-singular mass distributions near their center, while the solution domain extends many orders of magnitude larger than the radius of the distribution (to connect with flat space-time). Rotating solutions are found with very high central energy densities for a range of adiaba…
The recent detection of gravitational waves and electromagnetic counterparts emitted during and after the collision of two neutron stars marks a breakthrough in the field of multi-messenger astronomy. Numerical relativity simulations are the only tool to describe the binary's merger dynamics in the regime when speeds are largest and gravity is strongest. In this work we report state-of-the-art binary neutron star simulations for irrotational (non-spinning) and spinning configurations. The main use of these simulations is to model the gravitational-wave signal. Key numerical requirements are th…
We present fully general relativistic simulations of the quasi-circular inspiral and merger of charged, non-spinning, binary black holes with charge-to-mass ratio $λ\le 0.3$. We discuss the key features that enabled long term and stable evolutions of these binaries. We also present a formalism for computing the angular momentum carried away by electromagnetic waves, and the electromagnetic contribution to black-hole horizon properties. We implement our formalism and present the results for the first time in numerical-relativity simulations. In addition, we compare our full non-linear solutions…
We present fully general-relativistic numerical evolutions of self-gravitating tori around spinning black holes with dimensionless spin $a/M = 0.7$ parallel or anti-parallel to the disk angular momentum. The initial disks are unstable to the hydrodynamic Papaloizou-Pringle Instability which causes them to grow persistent orbiting matter clumps. The effect of black hole spin on the growth and saturation of the instability is assessed. We find that the instability behaves similarly to prior simulations with non-spinning black holes, with a shift in frequency due to spin-induced changes in disk o…
Gravitational-wave observations of binary black holes currently rely on theoretical models that predict the dominant multipoles (l,m) of the radiation during inspiral, merger and ringdown. We introduce a simple method to include the subdominant multipoles to binary black hole gravitational waveforms, given a frequency-domain model for the dominant multipoles. The amplitude and phase of the original model are appropriately stretched and rescaled using post-Newtonian results (for the inspiral), perturbation theory (for the ringdown), and a smooth transition between the two. No additional tuning …
The Mathisson-Papapetrou-Dixon (MPD) equations, providing the "pole-dipole" description of spinning test particles in general relativity, have to be supplemented by a condition specifying the worldline that will represent the history of the studied body. It has long been thought that the Mathisson-Pirani (MP) spin condition -- unlike other major choices made in the literature -- does not yield an explicit momentum-velocity relation. We derive here the desired (and very simple) relation and show that it is in fact equivalent to the MP condition. We clarify the apparent paradox between the exist…
We perform magnetohydrodynamic simulations of accreting, equal-mass binary black holes in full general relativity focusing on the effect of spin and minidisks on the accretion rate and Poynting luminosity variability. We report on the structure of the minidisks and periodicities in the mass of the minidisks, mass accretion rates, and Poynting luminosity. The accretion rate exhibits a quasi-periodic behavior related to the orbital frequency of the binary in all systems that we study, but the amplitude of this modulation is dependent on the existence of persistent minidisks. In particular, syste…
The production of numerical relativity waveforms that describe quasicircular binary black hole mergers requires high-quality initial data, and an algorithm to iteratively reduce residual eccentricity. To date, these tools remain closed source, or in commercial software that prevents their use in high performance computing platforms. To address these limitations, and to ensure that the broader numerical relativity community has access to these tools, herein we provide all the required elements to produce high-quality numerical relativity simulations in supercomputer platforms, namely: open sour…
Consistency of spin effects between numerical relativity and perturbation theory for inspiraling comparable-mass black hole binaries
Kavli Institute for Theoretical Physics, University of California Santa Barbara（加州大学圣塔芭芭拉分校卡弗里理论物理研究所）；University of Rhode Island（罗德岛大学）；University of Massachusetts, Dartmouth（马萨诸塞大学达特茅斯分校）
The last years have brought upon us a golden age of observational gravitational physics. The several observations by the LIGO/Virgo/KAGRA collaboration about gravitational waves and by the EHT collaboration about the shadow and lensing of light around the supermassive black hole in the centre of M87 will point the scientific community in the correct direction to find an answer to the Kerr hypothesis. In order to follow that direction, the systematic construction and analysis of the physical properties of solutions within General Relativity with additional fields or within modified theories of …
The advent of gravitational wave (GW) astronomy has provided us with observations of black holes more massive than those known from X-ray astronomy. However, the observation of an intermediate-mass black hole (IMBH) remains a big challenge. After their second observing run, the LIGO \& Virgo Scientific collaborations (LVC) placed upper limits on the coalescence rate density of non-precessing IMBH binaries (IMBHBs). In this article, we explore the sensitivity of two of the search pipelines used by the LVC to signals from 69 numerically simulated IMBHBs with generic spins, out of which 27 have a…
Recent progress on the description of relativistic spin: vector model of spinning particle and rotating body with gravimagnetic moment in General Relativity
Fokker action of non-spinning compact binaries at the fourth post-Newtonian approximation
本文在广义相对论的后牛顿第四近似（4PN）下，在调和坐标系中导出了无自旋紧致双星系统运动的Fokker作用量。维度正则化用于治疗与点粒子相关的局部紫外线（UV）发散，然后通过重整化的极点到一个重新定义的点质量的轨迹。与在无穷远传播的波尾相关的4PN阶的效应始终包括在动作的水平上。基于解析延拓的有限部分程序处理在空间无穷远的红外（IR）发散，这是完全一致的近区尾部的存在。我们的结果在4PN阶是洛伦兹不变的，并有正确的自力极限的圆形轨道的能量。然而，我们发现，它不同于最近发表的结果中的ADM哈密顿公式的广义相对论[T。Damour，P. Jaranowski，and G. Schäfer，Phys.Rev.D89，064058（2014）]。需要做更多的工作来理解这种差异。
This work is originally a Cambridge Part III essay. Throughout the paper, some aspects of General Relativity in higher dimensions are reviewed. The work presented draws a path within the wide landscape of higher dimensional black holes theory towards a specific objective: understanding how the combination of extended black objects and ultra-spinning rotation dynamics give rise to black hole topologies that depart from sphericity. The discussion aims to offer a compromise between giving a reasonably wide picture of the area of higher dimensional black holes, while at the same time going into de…
In the main article [CQG 38 (2021) 055003], a new "canonical" form for the Lewis metrics of the Weyl class has been obtained, depending only on three parameters -- Komar mass and angular momentum per unit length, plus the angle deficit -- corresponding to a coordinate system fixed to the "distant stars" and an everywhere timelike Killing vector field. Such form evinces the local but non-global static character of the spacetime, and striking parallelisms with the electromagnetic analogue. We discuss here its generality, main physical features and important limits (the Levi-Civita static cylinde…
