空间引力波观测站{ \emph{Laser Interferometer Space Antenna} }的主要目标之一是检验重力波的偏差。这是第一次，我们一贯计算产生的引力波极端质量比inspirals（恒星致密物体到超大质量黑洞）在一个动机良好的替代引力理论，迄今为止仍然弱约束双脉冲星观测。我们集中讨论的理论是Chern-Simons（CS）修正引力，这是一个四维的有效理论，它是由弦论和圈量子引力激发的，通过增加一个动力学标量场和宇称违反的庞特里亚金密度来增强Einstein-Hilbert作用量。我们表明，虽然点粒子继续遵循测地线在修改后的理论，他们的背景是一个修改的克尔度规，这印CS校正的引力波发射。CS修正的引力波与广义相对论的预期有很大的不同，即它们在3周的演化后会导致显著的失相，但这种失相可能不会阻止对这些信号的检测，而是会导致参数确定中的系统误差。最后，我们研究了辐射反应的修正理论，并表明，领先的顺序，能量动量发射没有CS修改，除了可能的标量场发射的次优势效应。包括辐射反应将允许测试CS修改重力与星载探测器，可能是两个数量级大于目前的双脉冲星的界限。
英文摘要：
Testing deviation of GR is one of the main goals of the proposed {\emph{Laser Interferometer Space Antenna}}, a space-based gravitational-wave observatory. For the first time, we consistently compute the generation of gravitational waves from extreme-mass ratio inspirals (stellar compact objects into supermassive black holes) in a well-motivated alternative theory of gravity, that to date remains weakly constrained by double binary pulsar observations. The theory we concentrate on is Chern-Simons (CS) modified gravity, a 4-D, effective theory that is motivated both from string theory and loop-quantum gravity, and which enhances the Einstein-Hilbert action through the addition of a dynamical scalar field and the parity-violating Pontryagin density. We show that although point particles continue to follow geodesics in the modified theory, the background about which they inspiral is a modification to the Kerr metric, which imprints a CS correction on the gravitational waves emitted. CS modified gravitational waves are sufficiently different from the General Relativistic expectation that they lead to significant dephasing after 3 weeks of evolution, but such dephasing will probably not prevent detection of these signals, but instead lead to a systematic error in the determination of parameters. We end with a study of radiation-reaction in the modified theory and show that, to leading-order, energy-momentum emission is not CS modified, except possibly for the subdominant effect of scalar-field emission. The inclusion of radiation-reaction will allow for tests of CS modified gravity with space-borne detectors that might be two orders of magnitude larger than current binary pulsar bounds.
Modeling Extreme Mass Ratio Inspirals within the Effective-One-Body Approach
我们提出了第一个模型的极端质量比的有效单体（EOB）的形式主义，专注于非旋转黑洞的准圆形轨道内的吸气。我们发现，经过2年的演化，解析EOB和基于Teukolsky的数值重力波形之间的相位差和（牛顿归一化）振幅差可以分别减小到小于10^（-1）rad和小于2 x 10^（-3）。在EOB方法中包含后牛顿自作用力项导致经过2年的演化后相位不一致约为6-27 rad。这样的包含物还可以允许来自中间质量比、准圆形吸气的波形的EOB建模。
The inspirals of stellar-mass mass compact objects into massive black holes in the centres of galaxies are one of the most important sources of gravitational radiation for space-based detectors like LISA or eLISA. These extreme-mass-ratio inspirals (EMRIs) will enable an ambitious research program with implications for astrophysics, cosmology, and fundamental physics. This article is a summary of the talks delivered at the plenary session on EMRIs at the 10th International LISA Symposium. It contains research updates on the following topics: astrophysics of EMRIs; EMRI science potential; and E…
We study Extreme Mass Ratio Inspirals (EMRIs), during which a small body spirals into a supermassive black hole, in gravity theories with additional scalar fields. We first argue that no-hair theorems and the properties of known theories that manage to circumvent them introduce a drastic simplification to the problem: the effects of the scalar on supermassive black holes, if any, are mostly negligible for EMRIs in vast classes of theories. We then exploit this simplification to model the inspiral perturbatively and we demonstrate that the scalar charge of the small body leaves a significant im…
Future space-based laser interferometry experiments such as LISA are expected to detect $\cal O$(100--1000) stellar-mass compact objects (e.g., black holes, neutron stars) falling into massive black holes in the centers of galaxies, the so-called extreme-mass-ratio inspirals (EMRIs). If dark matter forms a "spike" due to the growth of the massive black hole, it will induce a gravitational drag on the inspiraling object, changing its orbit and gravitational-wave signal. We show that detection of even a single dark matter spike from the EMRIs will severely constrain several popular dark matter c…
A compact object with a mass $\mathcal{O}(1 \sim 1000) M_{\odot}$, such as a black hole of stellar or primordial origin or a neutron star, and a much lighter exotic compact object with a subsolar mass could form a non-standard mini extreme mass ratio inspiral (EMRI) and emit gravitational waves within the frequency band of ground-based gravitational-wave detectors. These systems are extremely interesting because detecting them would definitively point to new physics. We study the capability of using LIGO/Virgo to search for mini-EMRIs and find that a large class of exotic compact objects can b…
The Laser Interferometer Space Antenna, LISA, will detect gravitational wave signals from Extreme Mass Ratio Inspirals, where a stellar mass compact object orbits a supermassive black hole and eventually plunges into it. Here we report on LISA's capability to detect whether the smaller compact object in an Extreme Mass Ratio Inspiral is endowed with a scalar field, and to measure its scalar charge -- a dimensionless quantity that acts as a measure of how much scalar field the object carries. By direct comparison of signals, we show that LISA will be able to detect and measure the scalar charge…
We study binary systems in which a stellar mass compact object spirals into a massive black hole, known as extreme mass ratio inspirals, in scenarios with a new fundamental scalar field. Earlier work has shown that, in most interesting such scenarios and to leading order in the mass ratio, the massive black holes can be adequately approximated by the Kerr metric and the imprint of the scalar field on the waveform is fully controlled by the scalar charge of the stellar mass object. Here we use this drastic simplification in the inspiral modelling and consider eccentric equatorial orbits. We stu…
In this article we consider prospects for detecting extreme mass ratio inspirals (EMRIs) using gravitational wave (GW) observations by a future space borne interferometric observatory eLISA. We start with a description of EMRI formation channels. Different formation scenarios lead to variations in the expected event rate and predict different distributions of the orbital parameters when the GW signal enters the eLISA sensitivity band. Then we will briefly overview the available theoretical models describing the GW signal from EMRIs and describe proposed methods for their detection.
We consider extreme mass ratio inspirals during which an electrically charged compact object with mass $m_p$ and the charge to mass ratio $q$ inspirals around a Schwarzschild black hole of mass $M$. Using the Teukolsky and generalized Sasaki-Nakamura formalisms for the gravitational and electromagnetic perturbations around a Schwarzschild black hole, we numerically calculate the energy flux of both gravitational and electromagnetic waves induced by a charged particle moving in circular orbits. With one year observation of these extreme mass ratio inspirals, we show that space-based gravitation…
An extreme mass ratio inspiral takes place when a compact stellar object is inspiraling into a supermassive black hole due to gravitational radiation reaction. Gravitational waves (GWs) from this system can be calculated using the Teukolsky equation (TE). In our case, we compute the asymptotic GW fluxes of a spinning body orbiting a Kerr black hole by solving numerically the TE both in time and frequency domain. Our ultimate goal is to produce GW templates for space-based detectors such as LISA.
The observation of the inspiral and merger of compact binaries by the LIGO/Virgo collaboration ushered in a new era in the study of strong-field gravity. We review current and future tests of strong gravity and of the Kerr paradigm with gravitational-wave interferometers, both within a theory-agnostic framework (the parametrized post-Einsteinian formalism) and in the context of specific modified theories of gravity (scalar-tensor, Einstein-dilaton-Gauss-Bonnet, dynamical Chern-Simons, Lorentz-violating, and extra dimensional theories). In this contribution we focus on (i) the information carri…
One of the main targets of the Laser Interferometer Space Antenna (LISA) is the detection of extreme mass-ratio inspirals (EMRIs) and extremely large mass-ratio inspirals (X-MRIs). Their orbits are expected to be highly eccentric and relativistic when entering the LISA band. Under these circumstances, the inspiral time-scale given by Peters' formula loses precision and the shift of the last-stable orbit (LSO) caused by the massive black hole spin could influence the event rates estimate. We re-derive EMRIs and X-MRIs event rates by implementing two different versions of a Kerr loss-cone angle …
The Kerr geometry admits the Carter symmetry, which ensures that the geodesic equations are integrable. It is shown that gravitational waveforms associated with extreme-mass-ratio inspirals involving a non-integrable compact object display `glitch' phenomena, where the frequencies of gravitational waves increase abruptly, when the orbit crosses certain spacetime regions known as Birkhoff islands. The presence or absence of these features in data from upcoming space-borne detectors will therefore allow not only for tests of general relativity, but also of fundamental spacetime symmetries.
Extreme mass ratio inspirals (EMRIs) show a strong separation of timescales, with the time characterizing inspiral, $T_{\rm i}$, much longer than any time $T_{\rm o}$ characterizing orbital motions. The ratio of these timescales (which is essentially an EMRI's mass ratio) can be regarded as a parameter that controls a perturbative expansion. Here we describe the value and limitations of an "adiabatic" description of these binaries, which uses only the leading terms arising from such a two-timescale expansion. An adiabatic approach breaks down when orbits evolve through resonances, with importa…
One of the key astrophysical sources for the Laser Interferometer Space Antenna (LISA) are the inspirals of stellar-origin compact objects into massive black holes in the centres of galaxies. These extreme-mass-ratio inspirals (EMRIs) have great potential for astrophysics, cosmology and fundamental physics. In this paper we describe the likely numbers and properties of EMRI events that LISA will observe. We present the first results computed for the 2.5 Gm interferometer that was the new baseline mission submitted in January 2017 in response to the ESA L3 mission call. In addition, we attempt …
Intermediate/Extreme mass ratio inspiral (I/EMRI) system provides a good tool to test the nature of gravity in strong field. Based on the method of osculating orbits, we compute the orbital evolutions of I/EMRIs on quasi-elliptic orbits in both Einstein's general relativity and Brans-Dicke theory. The extra monopolar and dipolar channels in Brans-Dicke theory accelerate the orbital decay, so it is important to consider the effects of monopolar and dipolar emissions on the waveform. With the help of accurate orbital motion, we generate waveform templates which include both monopolar and dipolar…
We investigate the possibility of sustained orbital resonances in extreme mass ratio inspirals. Using a near-identity averaging transformation, we reduce the equations of motion for a particle moving in Kerr spacetime with self-force corrections in the neighbourhood of a resonant geodesic to a one dimensional equation for a particle moving in an effective potential. From this effective equation we obtain the necessary and sufficient conditions that the self-force needs to satisfy to allow inspiralling orbits to be captured in sustained resonance. Along the way we also obtain the full non-linea…
The space based interferometer LISA will be capable of detecting the gravitational waves emitted by stellar mass black holes or neutron stars slowly inspiralling into the supermassive black holes found in the centre of most galaxies. The gravitational wave signal from such an extreme mass ratio inspiral (EMRI) event will provide a unique opportunity to test whether the spacetime metric around the central black hole is well described by the Kerr solution. In this paper a well studied model for EMRIs around Kerr black holes is extended to a family of parametrically deformed bumpy black holes whi…
Sequential simulation-based inference for extreme mass ratio inspirals
Università degli Studi di Milano-Bicocca（米兰比可卡大学）；INFN, Sezione di Milano-Bicocca（意大利国家核物理研究所米兰比可卡分部）；Kavli Institute for Cosmology Cambridge（剑桥卡弗里宇宙学研究所）；Institute of Astronomy, University of Cambridge（剑桥大学天文学研究所）；European Space Agency (ESA)（欧洲空间局）；University of Amsterdam（阿姆斯特丹大学）
Extreme-mass-ratio inspirals will be prized sources for the upcoming space-based gravitational-wave observatory LISA. The hunt for these is beset by many open theoretical and computational problems in both source modeling and data analysis. We draw attention here to one of the most poorly understood: the phenomenon of non-local correlations in the space of extreme-mass-ratio-inspiral signals. Such correlations are ubiquitous in the continuum of possible signals (degeneracy), and severely hinder the search for actual signals in LISA data. However, they are unlikely to manifest in a realistic se…
Extreme mass ratio inspirals (EMRIs) occur when a compact object orbits a much larger one, like a solar-mass black hole around a supermassive black hole. The orbit has 3 frequencies which evolve through the inspiral. If the orbital radial frequency and polar frequency become commensurate, the system passes through a transient resonance. Evolving through resonance causes a jump in the evolution of the orbital parameters. We study these jumps and their impact on EMRI gravitational-wave detection. Jumps are smaller for lower eccentricity orbits; since most EMRIs have small eccentricities when pas…
We investigate resonance crossings of a charged body moving around a Kerr black hole immersed in an external homogeneous magnetic field. This system can serve as an electromagnetic analogue of a weakly non-integrable extreme mass ratio inspiral (EMRI). In particular, the presence of the magnetic field renders the conservative part of the system non-integrable in the Liouville sense, while the electromagnetic self-force causes the charged body to inspiral. By studying the system without the self-force, we show the existence of an approximate Carter-like constant and discuss how resonances grow …
The detection of gravitational waves from extreme-mass-ratio inspirals with upcoming space-borne detectors will allow for unprecedented tests of general relativity in the strong-field regime. Aside from assessing whether black holes are unequivocally described by the Kerr metric, such detections may place constraints on the degree of spacetime symmetry. In particular, depending on exactly how a hypothetical departure from the Kerr metric manifests, the Carter symmetry, which implies the integrability of the geodesic equations, may be broken. Here, we examine the gravitational waveforms associa…
Future space-borne interferometers will be able to detect gravitational waves at $10^{-3}$ to $10^{-1}$ Hz. At this band extreme-mass-ratio inspirals (EMRIs) can be promising gravitational wave sources. In this paper, we investigate possibility of testing Kerr hypothesis against a parametrized non-Kerr metric by matching EMRI signals. However, EMRIs from either equatorial orbits or inclined orbits suffer from the "confusion problem". Our results show that, within the time scale before radiation flux plays an important role, small and moderate deviations from the Kerr spacetime($|δ_i|<1$) can b…
The post-Newtonian approximation is useful to discuss gravitational waveforms for binary inspirals. In this note, for retrograde circular orbits in the equatorial plane, we discuss the region of validity of the post-Newtonian approximation by using the gravitational energy flux derived numerically and analytically in the black hole perturbation approach. It is found that the edge of the allowable region behaves quite intricately, including prograde orbits even if we treat higher post-Newtonian orders.
The bumblebee gravity model, with a vector field nonminimally coupled to gravity, is a natural extension of the Einstein-Maxwell theory. In this theory, a black hole can carry a vector hair, making the metric deviate from the Schwarzschild metric. To investigate the detectability of the vector hair, we consider an Extreme Mass Ratio Inspiral (EMRI) system, where a stellar-mass black hole inspiraling into a supermassive black hole. We find that, with a one-year observation of an EMRI by a space-based gravitational-wave detector, we can probe the vector charge as small as $Q\sim 10^{-3}$ in the …
A number of open problems hinder our present ability to extract scientific information from data that will be gathered by the near-future gravitational-wave mission LISA. Many of these relate to the modeling, detection and characterization of signals from binary inspirals with an extreme component-mass ratio of $\lesssim10^{-4}$. In this paper, we draw attention to the issue of systematic error in parameter estimation due to the use of fast but approximate waveform models; this is found to be relevant for extreme-mass-ratio inspirals even in the case of waveforms with $\gtrsim90\%$ overlap acc…
It is known that massive black holes (MBHs) of $10^{5-7}\,M_\odot$ could capture small compact objects to form extreme-mass-ratio inspirals (EMRIs). Such systems emit gravitational waves (GWs) in the band of the Laser Interferometer Space Antenna (LISA) and are ideal probes of the space-time geometry of MBHs. Recently, we have shown that MBHs could also capture stellar-mass binary black holes (about $10\,M_\odot$) to form binary-EMRIs (b-EMRIs) and, interestingly, a large fraction of the binaries coalesce due to the tidal perturbation by the MBHs. Here we further show that the coalescence coul…
We estimate the accuracy in the measurement of the tidal Love number of a supermassive compact object through the detection of an extreme mass ratio inspiral~(EMRI) by the future LISA mission. A nonzero Love number would be a smoking gun for departures from the classical black hole prediction of General Relativity. We find that an EMRI detection by LISA could set constraints on the tidal Love number of a spinning central object with dimensionless spin $\hat a=0.9$ ($\hat a=0.99$) which are approximately four (six) orders of magnitude more stringent than what achievable with current ground-base…
