我们研究极端质量比 inspirals（EMRIs）作为探测超越真空广义相对论效应的探针，考虑了天体物理环境和标量 Gauss-Bonnet（sGB）引力。在超越真空场景中，一个浸在冷暗物质环境中的 EMRI 的演化会改变引力波通量并引入额外的耗散效应，如动态摩擦。同时，在 sGB 引力等超越广义相对论的设定中，绕行物体携带有效的标量电荷并发射标量辐射。环境和修改引力效应都会修改通量平衡定律，从而引起 EMRI 动力学的变化。利用固定频率形式中的双时间尺度分析，我们计算了准圆形、赤道轨道在静态、球对称时空中的 leading-order 修正能量通量，并构建了相应的引力波形，这些被用来量化相对于真空广义相对论情况的累积引力波退相和波形不匹配。我们进一步进行了 Fisher 信息矩阵分析，以估计参数相关性和未来空间基探测器如激光干涉仪空间天线（LISA）区分环境和修改引力效应的能力。我们的结果表明，暗物质和标量场效应都能在 EMRI 波形上留下可测量的印记，并且一致的超越真空处理对于稳健的引力测试至关重要。
英文摘要：
We examine extreme mass-ratio inspirals (EMRIs) as probes of beyond-vacuum general relativistic effects, accounting for both astrophysical environments and scalar Gauss-Bonnet (sGB) gravity. In beyond-vacuum scenarios, the evolution of an EMRI immersed in a cold dark matter environment modifies the gravitational wave flux and introduces additional dissipative effects such as dynamical friction. In parallel, in the beyond-general relativistic settings such as in sGB gravity, the inspiraling object carries an effective scalar charge and emits scalar radiation. Both environmental and modified-gravity effects modify the flux-balance law, thereby inducing changes in the EMRI dynamics. Using a two-timescale analysis within the fixed-frequency formalism, we compute leading-order corrections to the energy fluxes for quasi-circular, equatorial orbits in static, spherically symmetric spacetimes and construct the corresponding gravitational waveforms, which are used to quantify the accumulated gravitational wave dephasing and waveform mismatch relative to the vacuum general relativistic case. We further perform the Fisher Information Matrix analysis to estimate parameter correlations and the ability of future space-based detectors such as the Laser Interferometer Space Antenna (LISA) to disentangle environmental and modified gravity effects. Our results show that both dark matter and scalar field effects can leave measurable imprints on EMRI waveforms and that a consistent beyond-vacuum treatment is essential for robust tests of gravity.
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 …
Probing fundamental physics with Extreme Mass Ratio Inspirals: a full Bayesian inference for scalar charge
Max Planck Institute for Gravitational Physics (Albert Einstein Institute)（马克斯·普朗克引力物理研究所（阿尔伯特·爱因斯坦研究所））；School of Mathematical Sciences & School of Physics and Astronomy, University of Nottingham（诺丁汉大学数学科学学院与物理与天文学学院）；Nottingham Centre of Gravity, University of Nottingham（诺丁汉大学重力研究中心）；Gran Sasso Science Institute (GSSI)（格兰萨索科学研究所）；INFN, Laboratori Nazionali del Gran Sasso（意大利国家核物理研究所，格兰萨索国家实验室）；School of Mathematics and Statistics, University College Dublin（都柏林大学学院数学与统计学院）；Niels Bohr International Academy, Niels Bohr Institute（尼尔斯·玻尔国际学院，尼尔斯·玻尔研究所）；Department of Physics, National University of Singapore（新加坡国立大学物理系）；Department of Mathematics, National University of Singapore（新加坡国立大学数学系）；Laboratoire des 2 Infinis – Toulouse (L2IT-IN2P3), Universitè de Toulouse, CNRS（图卢兹双无穷实验室（L2IT-IN2P3），图卢兹大学，法国国家科学研究中心）
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 extreme-gravity collisions between black holes allow us to probe the underlying theory of gravity. We apply the theory-agnostic inspiral-merger-ringdown consistency test to an example theory beyond general relativity for the first time. Here we focus on the string-inspired Einstein-dilaton Gauss-Bonnet gravity and modify the inspiral, ringdown, and remnant black hole properties of the gravitational waveform. We found that future multiband observations allow us to constrain the theory stronger than current observations by an order of magnitude. The formalism developed here can easily be app…
A generalization of Ryan's theorem: probing tidal coupling with gravitational waves from nearly circular, nearly equatorial, extreme-mass-ratio inspirals
Under the framework of gravitational effective field theory, we propose a theory agnostic strategy of searching for higher-spin particles with gravitational waves from compact binary inspirals. Using this strategy, we analyze gravitational wave signals from the binary black hole merger events GW151226 and GW170608, as well as the binary neutron star merger event GW170817. We find that the existence of higher-spin particles with mass ranged from $10^{-12} {\rm eV}$ to $10^{-11} {\rm eV}$ is strongly disfavored by these events unless the particles precisely combine within a supersymmetric superm…
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.
Probing near-zone magnetic fields with extreme mass-ratio inspirals
School of Physics and Optoelectronics, South China University of Technology（华南理工大学物理与光电工程学院）；Department of physics, Nanchang University（南昌大学物理系）；Center for Relativistic Astrophysics and High Energy Physics, Nanchang University（南昌大学相对论天体物理与高能物理中心）
In the Galaxy, extremely large mass-ratio inspirals(X-MRIs) composed of brown dwarfs and the massive black hole at the Galactic Center are expected to be promising gravitational wave sources for space-borne detectors. In this work, we simulate the gravitational wave signals from twenty X-MRI systems by an axisymmetric Konoplya-Rezzolla-Zhidenko metric with varied parameters. We find that the mass, spin, and deviation parameters of the Kerr black hole could be determined accurately ( $\sim 10^{-5} - 10^{-6}$ ) with only one X-MRI event with a high signal-to-noise ratio. The measurement of the a…
The "flux-balance formulae" that determine the averaged evolution of energy, azimuthal angular momentum, and Carter constant in terms of the averaged asymptotic gravitational-wave fluxes for inspirals of small bodies into Kerr black holes were first derived about 15 years ago. However, this derivation is restricted to the case that the background Kerr geodesics are non-resonant (i.e., the radial and angular motions are always incommensurate), and excludes the resonant case that can be important for the radiative dynamics of extreme mass-ratio inspirals. We give here a new derivation of the flu…
How to calculate the gravitational waves (GWs) of Extreme-mass-ratio-inspirals (EMRIs) in a highly accurate and efficient way still keeps a challenge. In this paper, we present a so-called fully recalibrated waveforms for EMRIs with high accuracy. Based on the numerical data by solving the Teukolsky equations, we recalibrate all mass-ratio independent coefficients of the factorized waveforms which are used in the effective-one-body (EOB) models. Due to these new coefficients, the precision of waveforms is improved enormously, and is much higher than the original forms and at the same time high…
We describe a new class of resonances for extreme mass-ratio inspirals (EMRIs): tidal resonances, induced by the tidal field of nearby stars or stellar-mass black holes. A tidal resonance can be viewed as a general relativistic extension of the Kozai-Lidov resonances in Newtonian systems, and is distinct from the transient resonance already known for EMRI systems. Tidal resonances will generically occur for EMRIs. By probing their influence on the phase of an EMRI waveform, we can learn about the tidal environmental of the EMRI system, albeit at the cost of a more complicated waveform model. O…
In general relativity, there is no dispersion in gravitational waves, while some modified gravity theories predict dispersion phenomena in the propagation of gravitational waves. In this paper, we demonstrate that this dispersion will induce an observable deviation of waveforms if the orbits have large eccentricities. The mechanism is that the waveform modes with different frequencies will be emitted at the same time due to the existence of eccentricity. During the propagation, because of the dispersion, the arrival time of different modes will be different, then produce the deviation and deph…
Extreme mass ratio inspirals (EMRIs) will be important sources for future space-based gravitational-wave detectors. In recent work, tidal resonances in binary orbital evolution induced by the tidal field of nearby stars or black holes have been identified as being potentially significant in the context of extreme mass-ratio inspirals. These resonances occur when the three orbital frequencies describing the orbit are commensurate. During the resonance, the orbital parameters of the small body experience a jump leading to a shift in the phase of the gravitational waveform. In this paper, we trea…
In certain models of a QCD axion, finite density corrections to the axion potential can result in the axion being sourced by large dense objects. There are a variety of ways to test this phenomenon, but perhaps the most surprising effect is that the axion can mediate forces between neutron stars that can be as strong as gravity. These forces can be attractive or repulsive and their presence can be detected by Advanced LIGO observations of neutron star inspirals. By a numerical coincidence, axion forces between neutron stars with gravitational strength naturally have an associated length scale …
In this paper, we study gravitational waves generated by binary systems within an extension of General Relativity which is described by the addition of quadratic in curvature tensor terms to the Einstein-Hilbert action. Treating quadratic gravity as an effective theory valid in the low energy/curvature regime, we argue that reliable calculations can be performed in the early inspiral phase, and furthermore, no flux of additional massive waves can be detected. We then compute the massive dipole (-1PN) leading corrections to the post-Newtonian (PN) expansion of the standard waveform. By confront…
We revisit the accuracy of the post-Newtonian (PN) approximation and its region of validity for quasi-circular orbits of a point particle in the Kerr spacetime, by using an analytically known highest post-Newtonian order gravitational energy flux and accurate numerical results in the black hole perturbation approach. It is found that regions of validity become larger for higher PN order results although there are several local maximums in regions of validity for relatively low-PN order results. This might imply that higher PN order calculations are also encouraged for comparable-mass binaries.
Future space-borne gravitational-wave detectors will observe the gravitational waves in the milli-Hz. Extreme-mass-ratio inspirals with central supermassive black holes are very important sources that could provide the information of the vicinity of black holes. The event horizon separates the inner region of a black hole and there is nothing that can escape from this region. When the central supermassive compact object is a regular and horizonless rotating boson star, a small body could pass through the center and follow novel types of orbits. These will generate the gravitational waves that …
In this paper we discuss the development of a fast and accurate waveform model for the quasi-circular orbital evolution of extreme-mass-ratio-inspirals (EMRIs). This model simply employs the data of a few numerical Teukoulsky-based energy fluxes and waveforms to fit out a set of polynomials for the entire fluxes and waveforms. These obtained polynomials are accurate enough in the entire evolution domain, and much more accurate than the resummation post-Newtonian (PN) energy fluxes and waveforms, especially when the spin of a black hole becomes large. The dynamical equation we adopted for orbit…
Gravitational waves from extreme gravity events such as the coalescence of two black holes in a binary system fill our observable universe, bearing with them the underlying theory of gravity driving their process. One compelling alternative theory of gravity -- known as Einstein-dilaton Gauss-Bonnet gravity motivated by string theory -- describes the presence of an additional dilaton scalar field coupled directly to higher orders of the curvature, effectively describing a "fifth force" interaction and the emission of scalar dipole radiation between two scalarized black holes. Most previous stu…
In this work we analyze some judiciously chosen solutions of Kerr Black Holes with Scalar Hair (KBHsSH) of special interest for Gravitational Wave (GW) events originated from Extreme Mass Ratio Inspirals (EMRIs). Because of the off-center distribution of energy density, these spacetimes are warped in such a way that not all metric functions behave monotonically on the equatorial plane as in the exterior region of Kerr black holes (KBHs). This has great impact on the orbital parameters, which in turn affects the imprints on signals descendant from EMRIs in a adiabatic evolution. By investigatin…
The future space-borne detectors will provide the possibility to detect gravitational waves emitted from extreme mass ratio inspirals of stellar-mass compact objects into supermassive black holes. It is natural to expect that the spin of the compact object and cosmological constant will affect the orbit of the inspiral process and hence lead to the considerable phase shift of the corresponding gravitational waves. In this paper, we investigate the motion of a spinning test particle in the spinning black hole background with a cosmological constant and give the order of motion deviation induced…
We compute gravitational waves from inspiraling stellar-mass compact objects on the equatorial plane of a massive spinning black hole (BH). Our inspiral orbits are computed by taking into account the adiabatic change of orbital parameters due to gravitational radiation in the lowest order in mass ratio. We employ an interpolation method to compute the adiabatic change at arbitrary points inside the region of orbital parameter space computed in advance. Using the obtained inspiral orbits and associated gravitational waves, we compute power spectra of gravitational waves and the signal-to-noise …
