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The gravitational wave (GW) signal from the merger of two black holes can serve as a standard sirens for cosmological inference. However, a degeneracy exists between the luminosity distance and the inclination angle between the binary system's orbital angular momentum and the observer's line of sight, limiting the precise measurement of the luminosity distance. In this study, we investigate how higher harmonics affect luminosity distance estimation for third-generation (3G) GW detectors in binary black hole mergers. Our findings demonstrate that considering higher harmonics significantly enhances distance inference results compared with using only the (2,2) mode. This improved accuracy in distance estimates also strengthens constraints on host galaxies, enabling more precise measurements of the Hubble constant. These results highlight the significant influence of higher harmonics on the range estimation accuracy of 3G ground-based GW detectors., Comment: 14 pages, 6 figures

In the framework of general relativity (GR), gravitational waves (GWs) are theorized to travel at the speed of light across all frequencies. However, Lorentz invariance (LI) violation and weak equivalence principle (WEP) violation may lead to frequency-dependent variations in the propagation speed of GWs, which can be examined by comparing the theoretical and observed discrepancies in the arrival times of GW signals at various frequencies. This provides us with an opportunity to test these theories. In theories involving LI violations, we focus on the massive gravity with the graviton mass $m_g$. In the case of WEP violation, different massless particles exposed to the same gravitational source should exhibit varying gravitational time delays. The gravitational time delay induced by massive gravitational sources is proportional to $\gamma+1$, where the parameter $\gamma=1$ in GR. Therefore, we can quantify these two violations using the graviton mass $m_g$ and $|\Delta \gamma|$, respectively. In this study, we use selected GW data from binary black hole coalescences in the LIGO-Virgo catalogs GWTC-2.1 and GWTC-3 to place constraints on the parameters $m_g$ and $|\Delta \gamma|$. Our most stringent constraints suggest that $m_g \lesssim 1.40\times10^{-26}eV/c^2$ at the upper limit of the 90% credible interval and $|\Delta \gamma| \lesssim 7.05 \times 10^{-16}$ at the 90% credible interval. We also compute Bayes factors for models that assume LI and WEP violations compared to the standard GW model, respectively. The absolute value of the natural logarithm of the Bayes factor is generally less than 2. Our analysis reveals no statistically significant preference for either model. Additionally, the Bayes factors between these two models do not provide obvious evidence in favor of either one., Comment: 10 pages, 9 figures

The astrophysical origin of binary black hole (BBH) mergers remains uncertain though many events have been observed by the LIGO-Virgo-KAGRA network. Such mergers are predicted to originate in the vicinity of massive black holes (MBHs). Especially, GW190814, due to its secondary mass and mass ratio being beyond the expectations of isolated stellar evolution theories, is a promising event that has happened in an active galactic nucleus(AGN) disk. In this model, a compact object resides in the vicinity of a merging BBH. Here we report multiple pieces of evidence pointing to the fact that GW190814 is a BBH merging near a compact object. The orbital motion of BBHs around the third body produces a line-of-sight acceleration (LSA) and induces a varying Doppler shift. Using a waveform template that considers LSA, we perform Bayesian inference on a few BBH events with a high signal-to-noise ratio in the gravitational-wave transient catalog (GWTC). Compared to the model for isolated BBH mergers, we obtain significantly higher network signal-to-noise ratios for GW190814 by that with the LSA and constrain the LSA to $a = 0.0014^{+0.0014}_{-0.0022} ~c~\mathrm{s}^{-1}$. In addition, the logarithmic Bayes factor for the LSA case over the isolated case is $16.6$, which means the LSA model is significantly preferred by the GW data. We conclude that this is the first indication showing merging BBHs are located near a compact object., Comment: 19 pages, 4 figures

Detecting the environment around the supermassive black holes and tests of general relativity are important applications of extreme-mass-ratio inspirals (EMRIs). There is still a challenge to efficiently describe various "dirty" impacts on the inspirals like dark matter, gas, dipole radiation, electromagnetic interaction, and so on. In this Letter, we find the inherent linearity of the asymptotic solution of the inhomogeneous Teukolsky equation. Based on this property, we completely decouple the factors of the perturber and the background spacetime in the energy fluxes and waveforms. With the new decoupling form, the waveforms of EMRIs with non-geodesic motion in Kerr spacetime can be calculated conveniently. This will help to resolve the environment (including gas, field, dark matter, electromagnetic interaction, etc.) around the supermassive black holes and test general relativity., Comment: 6 pages + supplementary materials, 4 figures

Test of the no-hair theorem is the primary target with gravitational waves from binary black holes. In this Letter, we analyze gravitational-wave data from the LIGO-Virgo-KAGRA detection of binary black-hole mergers using the PSI_FD model, which is a non-general relativity full waveform template for arbitrary axisymmetric black holes. By analyzing two high signal-noise-ratio events, GW150914 and GW200129, the no-hair theorem is tested at a significance level of 95%, which is the best constraint until now. Especially, we find a significant deviation from the Kerr black hole in GW200129. More events and further analysis are needed to validate this deviation., Comment: 5 pages, 4 figures and 1 table

Binary neutron star mergers are unique sources of gravitational waves in multi-messenger astronomy. The inspiral phase of binary neutron stars can emit gravitational waves as chirp signals. The present waveform models of gravitational wave only considered the gravitational interaction. In this paper, we derive the waveform of the gravitational wave signal taking into account the presence of magnetic fields. We found that the electromagnetic interaction and radiation can introduce different frequency-dependent power laws for both amplitude and frequency of the gravitational wave. We show from the results of Fisher information matrix that the third-generation observation may detect magnetic dipole moments if the magnetic field is around 10^17 G.

The principal energy loss mechanism in a Nambu-Goto cosmic string network involves loop production and the subsequent gravitational-wave emission. Recently, it has been shown that the loop oscillations produce repeated gravitational-wave bursts emitted at cusps. The calculations are extended to estimate the number of burst repeaters, including kink emissions and kink-kink collisions. Our findings indicate that despite the potentially large number of kinks, we anticipate observing a higher number of burst repeaters from cusps for both LIGO-Virgo-KAGRA and the Laser Interferometer Space Antenna. We also conduct calculations using the second main loop distribution model in the current literature. We find that this model predicts a notably higher number of repeaters, which provides a reason to include it in future data analysis. These results offer insights into the potential observability of different loop features for future detectors, such as the space-based laser interferometers Taiji and TianQin., Comment: 7 pages, 4 figures

LISA, the Laser Interferometer Space Antenna, will usher in a new era in gravitational-wave astronomy. As the first anticipated space-based gravitational-wave detector, it will expand our view to the millihertz gravitational-wave sky, where a spectacular variety of interesting new sources abound: from millions of ultra-compact binaries in our Galaxy, to mergers of massive black holes at cosmological distances; from the beginnings of inspirals that will venture into the ground-based detectors' view to the death spiral of compact objects into massive black holes, and many sources in between. Central to realising LISA's discovery potential are waveform models, the theoretical and phenomenological predictions of the pattern of gravitational waves that these sources emit. This white paper is presented on behalf of the Waveform Working Group for the LISA Consortium. It provides a review of the current state of waveform models for LISA sources, and describes the significant challenges that must yet be overcome., Comment: 239 pages, 11 figures, white paper from the LISA Consortium Waveform Working Group, invited for submission to Living Reviews in Relativity, updated with comments from community

Gravitational waves (GWs) from binary black hole mergers provide unique opportunities for cosmological inference such as standard sirens. However, the accurate determination of the luminosity distance of the event is limited by the correlation between the distance and the angle between the binary's orbital angular momentum and the observer's line of sight. In the letter, we investigate the effect of precession on the distance estimation of binary black hole events for the third-generation (3G) GW detectors. We find that the precession can enhance the precision of distance inference by one order of magnitude compared to the scenario where precession is absent. The constraint on the host galaxies can be improved due to the improved distance measurement, therefore the Hubble constant can be measured with higher precision and accuracy. These findings underscore the noteworthy impact of precession on the precision of distance estimation for 3G ground-based GW detectors, which can serve as highly accurate probes of the Universe., Comment: 6 pages, 6 figures

One of the primary objectives for space-borne gravitational wave detectors is the detection of extreme-mass-ratio inspirals (EMRIs). This undertaking poses a substantial challenge because of the complex and long EMRI signals, further complicated by their inherently faint signal. In this research, we introduce a 2-layer Convolutional Neural Network (CNN) approach to detect EMRI signals for space-borne detectors. Our method employs the Q-transform for data preprocessing, effectively preserving EMRI signal characteristics while minimizing data size. By harnessing the robust capabilities of CNNs, we can reliably distinguish EMRI signals from noise, particularly when the signal-to-noise~(SNR) ratio reaches 50, a benchmark considered a ``golden'' EMRI. At the meantime, we incorporate time-delay interferometry (TDI) to ensure practical utility. We assess our model's performance using a 0.5-year dataset, achieving a true positive rate~(TPR) of 94.2\% at a 1\% false positive rate~(FPR) across various signal-to-noise ratio form 50-100, with 91\% TPR and 1\% FPR at an SNR of 50. This study underscores the promise of incorporating deep learning methods to advance EMRI data analysis, potentially leading to rapid EMRI signal detection., Comment: 12 pages, 8 figures, 2 tables

The Johannsen black hole (BH) is a generic rotating BH admitting three constants of motions (energy, angular momentum, and Carter constant) and is characterized by four deviation parameters besides mass and spin, which could be a model-independent probe of the no-hair theorem. We systematically study the dynamics of null particles around Johannsen BH, revealing the effects of the deviation parameters on the BH shadow as well as the effects of spin. By using the shadow boundaries of M87* and SgrA*, for the first time, the deviation parameters of those BHs are constrained. The detailed results depend on the spin $a$ and inclination angle $ \theta_0$. Assuming $a=0.2$ and $\theta_0=15^{\circ}$, the deviation parameter $\alpha_{13}$ are constained within $\sim $ [-3.5, 6] for M87* observation and [-3, 0.5] for SgrA* observation. We also show the images of a Johannsen BH surrounded by a Page-Thorne thin accretion disk observed by a remote observer with a ray-tracing method and discuss the effects of the deviation parameters on deforming the accretion disk image, which could be tested by observations with higher sensitivities in the future., Comment: 20 pages, 9 figures

In this work, we present a non-GR full waveform for general parametrization of axisymmetric black holes by extending our previous PSI model. Our model comprises two main components: an inspiral part obtained by using phenomenological method in frequency-domain and a ringdown part derived from quasinormal modes associated with photon motion. For quantitatively revealing the influence of the deviation from Kerr black holes on the waveforms, we specify our model to the bumpy black holes, which are typical examples of non-GR black holes. The results show that the deviation from the Kerr quadrupole moment could be measured in a high accuracy. The new waveform model can be directly used to test black holes for the LIGO-Virgo-KAGRA observations, the third generation detectors and space-borne interferometers., Comment: 14 pages, 17 figures

The popular waveform templates of extreme-mass-ratio inspirals usually omit the mass-ratio corrections in the conservative dynamics, and employ adiabatic approximation to include the radiation reaction. With the help of effective-one-body dynamics, we investigate the influence of mass-ratio corrections in the conservative part on the gravitational waves. We find that for the extra-relativistic orbits, the mass-ratio corrections can produce obvious orbital dephasing even for very small mass-ratio and then affect the waveforms. More importantly, it is noted that omitting the mass-ratio corrections in waveform templates may induce a fake signal of deviation from general relativity.

The direct observation of gravitational waves (GWs) opens a new window for exploring new physics from quanta to cosmos and provides a new tool for probing the evolution of universe. GWs detection in space covers a broad spectrum ranging over more than four orders of magnitude and enables us to study rich physical and astronomical phenomena. Taiji is a proposed space-based GW detection mission that will be launched in the 2030s. Taiji will be exposed to numerous overlapping and persistent GW signals buried in the foreground and background, posing various data analysis challenges. In order to empower potential scientific discoveries, the Mock LISA Data Challenge and the LISA Data Challenge (LDC) were developed. While LDC provides a baseline framework, the first LDC needs to be updated with more realistic simulations and adjusted detector responses for Taiji's constellation. In this paper, we review the scientific objectives and the roadmap for Taiji, as well as the technical difficulties in data analysis and the data generation strategy, and present the associated data challenges. In contrast to LDC, we utilize second-order Keplerian orbit and second-generation time delay interferometry techniques. Additionally, we employ a new model for the extreme-mass-ratio inspiral waveform and stochastic GW background spectrum, which enables us to test general relativity and measure the non-Gaussianity of curvature perturbations. Furthermore, we present a comprehensive showcase of parameter estimation using a toy dataset. This showcase not only demonstrates the scientific potential of the Taiji Data Challenge but also serves to validate the effectiveness of the pipeline. As the first data challenge for Taiji, we aim to build an open ground for data analysis related to Taiji sources and sciences. More details can be found on the official website at http://taiji-tdc.ictp-ap.org., Comment: 15 pages, 3 figures

The nature of black holes is one of most exciting issues in gravitational physics. If there is an exotic compact object as the compact as a black hole but without a horizon, gravitational wave echoes may be produced after the merger. In this work, we show that for extreme-mass-ratio binaries, even during the inspiraling phase of compact binary coalescence, the exists of hard surface of the exotic compact object will produce detectable signals on the gravitational waves. We predict that once the LIGO-Virgo-KAGRA, Einstein Telescope or Cosmic Explorer detect such kind of sources, our model shows that one can constrain the properties of surfaces of the compact objects in inspiraling stage better than the current level.

Many Hamiltonian problems in the Solar System are separable or separate into two analytically solvable parts, and thus give a great chance to the development and application of explicit symplectic integrators based on operator splitting and composing. However, such constructions cannot in general be available for curved spacetimes in general relativity and modified theories of gravity, because these curved spacetimes correspond to nonseparable Hamiltonians without the two part splits. Recently, several black hole spacetimes such as the Schwarzschild black hole were found to allow the construction of explicit symplectic integrators, since their corresponding Hamiltonians are separable into more than two explicitly integrable pieces. Although some other curved spacetimes including the Kerr black hole do not exist such multi part splits, their corresponding appropriate time transformation Hamiltonians do. In fact, the key problem for the obtainment of symplectic analytically integrable decomposition algorithms is how to split these Hamiltonians or time transformation Hamiltonians. Considering this idea, we develop explicit sympelcetic schemes in curved spacetimes. We introduce a class of spacetimes whose Hamiltonians are directly split into several explicitly integrable terms. For example, the Hamiltonian of rotating black ring has a 13 part split. We also present two sets of spacetimes whose appropriate time transformation Hamiltonians have the desirable splits. For instance, an 8 part split exists in a time-transformed Hamiltonian of Kerr-Newman solution with disformal parameter. In this way, the proposed symplectic splitting methods will be used widely for long-term integrations of orbits in most curved spacetimes we have known., Comment: 16pages,accepted by Astrophysical Journal

Extreme mass-ratio inspirals (EMRIs) are promising gravitational wave (GW) sources for space-based GW detectors. EMRI signals typically have long durations, ranging from several months to several years, necessitating highly accurate GW signal templates for detection. In most waveform models, compact objects in EMRIs are treated as test particles, without accounting for their spin, mass quadrupole, or tidal deformation. In this study, we simulate GW signals from EMRIs by incorporating the spin and mass quadrupole moments of the compact objects. We evaluate the accuracy of parameter estimation for these simulated waveforms using the Fisher Information Matrix (FIM) and find that the spin, tidal-induced quadruple, and spin-induced quadruple can all be measured with precision ranging from $10^{-2}$ to $10^{-1}$, particularly for a mass ratio of $\sim 10^{-4}$. Assuming the "true" GW signals originate from an extended body inspiraling into a supermassive black hole, we compute the signal-to-noise ratio (SNR) and Bayes factors between a test-particle waveform template and our model, which includes the spin and quadrupole of the compact object. Our results show that the spin of compact objects can produce detectable deviations in the waveforms across all object types, while tidal-induced quadrupoles are only significant for white dwarfs, especially in cases approaching an intermediate mass ratio. Spin-induced quadrupoles, however, have negligible effects on the waveforms. Therefore, our findings suggest that it is possible to distinguish primordial black holes from white dwarfs, and, under certain conditions, neutron stars can also be differentiated from primordial black holes., Comment: 18 pages, 9 figures

It is still an open issue if astrophysical black holes have electric charges or not. In this work, we analytically calculate gravitational and electromagnetic waveforms in the frequency domain for charged black hole binaries during the inspiral phase. In addition to the well-known $f^{-7/6}$ waveforms, we also get a $-11/6$ power law gravitational wave component. The phase of waveforms for charged binary is fully derived. In the case of electromagnetic counterparts, we focus on the electromagnetic dipole radiation, but we include the quadrupole contribution to complete our discussion. We also obtain the chirp property of the electromagnetic waves. In the case of dipole radiation, the frequency-domain waves are proportional to $f^{-7/6}$, while $f^{-1/6}$ appears in the quadrupole contribution. The frequency-domain waveforms can be used to estimate the charges of black holes in the current gravitational wave observations., Comment: 24 pages, 7 figures

We consider a black hole mimicker given by an exact solution of the stationary and axially symmetric field equations in vacuum known as the $\delta$-Kerr metric. We study its optical properties based on a ray-tracing code for photon motion and characterize the apparent shape of the shadow of the compact object and compare it with the Kerr black hole. For the purpose of obtaining qualitative estimates related to the observed shadow of the supermassive compact object in the galaxy M87 we focus on values of the object's spin $a$ and inclination angle of observation $\theta_0$ close to the measured values. We then apply the model to the shadow of the $\delta$-Kerr metric to obtain onstraints on the allowed values of the deformation parameter. We show that based uniquely on one set of observations of the shadow's boundary it is not possible to exclude the $\delta$-Kerr solution as a viable source for the geometry in the exterior of the compact object., Comment: 15 pages, 7 figures

Gravitational waves from precessing binary black holes exhibit new features that are absent in non-precessionary systems. All current waveform models take into account only the modulation of the signal due to precession. In this letter, we find that this effect has its own signature, by gravitational emission of a short and transient signal, or burst. The frequency of the burst is comparable to that of the late stage of the inspiral. We show that under certain conditions, this signal is strong enough to be detected by Advanced LIGO. For third-generation detectors like the Einstein telescope, the calculated signal-to-noise ratio can reach higher values. Measurements of precession would provide valuable insights into the intrinsic structure of black holes, and therefore into astrophysical binary formation mechanisms., Comment: 5 pages, 2 figures

In this work, we investigated the motion of spinning test particles around a rotating wormhole, extending, in this way, the previous work of Benavides-Gallego et al. in [Phys. Rev. D 101, no.12, 124024] to the general case. Using the Mathisson-Papapetrous-Dixon equations, we study the effective potential, circular orbits, and the innermost stable circular orbit (ISCO) of spinning test particles. We found that both the particle and wormhole spins affect the location of the ISCO significantly. On the other hand, Similar to the non-rotating case, we also found two possible configurations in the effective potential: plus and minus. Furthermore, the minimum value of the effective potential is not at the throat due to its spin, in contrast to the motion of the non-spinning test particles in a non-rotating wormhole, where the effective potential is symmetric, and its minimum value is at the throat. In the case of the ISCO, we found that it increases as the spin of the wormhole a increases, in contrast to black holes where the presence of spin decreases the value of the ISCO. Finally, since the dynamical four-momentum and kinematical four-velocity of the spinning particle are not always parallel, we consider the superluminal bound, finding that the allowed values of s change as the wormhole's spin a increases., Comment: 20 pages, 16 figures

The Laser Interferometer Space Antenna (LISA) has the potential to reveal wonders about the fundamental theory of nature at play in the extreme gravity regime, where the gravitational interaction is both strong and dynamical. In this white paper, the Fundamental Physics Working Group of the LISA Consortium summarizes the current topics in fundamental physics where LISA observations of GWs can be expected to provide key input. We provide the briefest of reviews to then delineate avenues for future research directions and to discuss connections between this working group, other working groups and the consortium work package teams. These connections must be developed for LISA to live up to its science potential in these areas., Comment: Accepted in: Living Reviews in Relativity

In this work, we discuss the improvement that the joint network of LISA and Taiji could provide on exploring two kinds of black hole formation mechanisms. For astrophysical origin, we consider light seed and heavy seed scenarios, and generate populations accordingly. We find that the joint network has the potential to observe growing light seeds in the range 15 < z < 20, while single detector can hardly see, which would shed light on the light seeding mechanism. For the heavy seeds, the joint network only improves the signal-to-noise ratio. For primordial origin, we calculate the event rate at z > 20 and detection rates of LISA and the joint network. The joint network expands LISA's horizon towards lower mass end, where the event rate is high, so we have better chance observing primordial black holes with the joint network. We also estimate the parameters using Fisher matrices of LISA and the joint network, and find that the joint network significantly improves the estimation., Comment: 8 pages, 13 figures

The waveforms from binary black hole mergers include inspiral, merger, and ringdown parts. Usually, the inspiral waveform can be obtained by calibrating from post-Newtonian approximation; The merger and ringdown ones can be gotten from the quasinormal modes with black hole perturbation theory. However, for more general black holes, the calculation of the quasinormal modes is not trivial. In this paper we use the photon sphere to get the quasinormal modes of spinning black holes. Then we connect the ringdown wave with the inspiral part to get full waveforms and compare with the ones from numerical relativity. We find that they match with each other very well. In principle this method can be extended to some general compact objects. As an example, the ringdown waveforms from parametrized axisymmetric black holes are obtained. We also use this method to get the ringdown signals of the accelerating final black hole; this is due to gravitational recoil during the merger. Even for the extreme cases, the acceleration due to the recoil cannot produce detectable effects., Comment: 14 pages, 12 figures

The Laser Interferometer Space Antenna (LISA) will be a transformative experiment for gravitational wave astronomy, and, as such, it will offer unique opportunities to address many key astrophysical questions in a completely novel way. The synergy with ground-based and space-born instruments in the electromagnetic domain, by enabling multi-messenger observations, will add further to the discovery potential of LISA. The next decade is crucial to prepare the astrophysical community for LISA's first observations. This review outlines the extensive landscape of astrophysical theory, numerical simulations, and astronomical observations that are instrumental for modeling and interpreting the upcoming LISA datastream. To this aim, the current knowledge in three main source classes for LISA is reviewed; ultracompact stellar-mass binaries, massive black hole binaries, and extreme or intermediate mass ratio inspirals. The relevant astrophysical processes and the established modeling techniques are summarized. Likewise, open issues and gaps in our understanding of these sources are highlighted, along with an indication of how LISA could help making progress in the different areas. New research avenues that LISA itself, or its joint exploitation with upcoming studies in the electromagnetic domain, will enable, are also illustrated. Improvements in modeling and analysis approaches, such as the combination of numerical simulations and modern data science techniques, are discussed. This review is intended to be a starting point for using LISA as a new discovery tool for understanding our Universe.

Electromagnetic counterparts of gravitational wave events usually involve neutron stars during compact binary coalescences. On the other hand, the community generally believes that electromagnetic emissions are hardly generated during the mergers of binary black holes. Nevertheless, some authors have considered the possibility of an EM counterpart signal after the GW150914, opening the opportunity to investigate the electromagnetic emission of stellar-mass black holes (BHs) mergers. In the case of black holes in a strong magnetic field or with electric charges, electromagnetic emissions would appear accompanied by gravitational waves. In this work, based on the membrane paradigm, we consider a phenomenological model to study the electromagnetic radiation generated by binary black holes surrounded by a uniform magnetic field. We obtain the electromagnetic waveform detected by a far-distance observer for varied black hole spins. By analytical Fourier transformation, we get the chirp property of the electromagnetic waves; we found that the power-law is 5/6, which has the opposite sign compared to gravitational waves. The frequency of such electromagnetic waves is the same as gravitational waves., Comment: 20 pages, 8 figures

In previous work [1], three TAIJI orbital deployments have been proposed to compose alternative LISA-TAIJI networks, TAIJIm (leading the Earth by $20^\circ$ and $-60^\circ$ inclined with respect to ecliptic plane), TAIJIp (leading the Earth by $20^\circ$ and $+60^\circ$ inclined), TAIJIc (colocated and coplanar with LISA) with respect to the LISA mission (trailing the Earth by $20^\circ$ and $+60^\circ$ inclined). And the LISA-TAIJIm network has been identified as the most capable configuration for massive black hole binary observation. In this work, we examine the performance of three networks to the stochastic gravitational wave background (SGWB) especially for the comparison of two eligible configurations, LISA-TAIJIm and LISA-TAIJIp. This investigation shows that the detectability of LISA-TAIJIm is competitive with the LISA-TAIJIp network for some specific SGWB spectral shapes. And the capability of LISA-TAIJIm is also identical to LISA-TAIJIp to separate the SGWB components by determining the parameters of signals. Considering the performances on SGWB and massive black hole binaries observations, the TAIJIm could be recognized as an optimal option to fulfill joint observations with LISA., Comment: 16 pages, 9 figures, accepted for publication in PRD

The motion of spinning test particles around a traversable wormhole is investigated using the Mathisson Papapetrous Dixon equations, which couple the Riemann tensor with the antisymmetric tensor $S^{ab}$, related to the spin of the particle. Hence, we study the effective potential, circular orbits, and innermost stable circular orbit ISCO of spinning particles. We found that the spin affects significantly the location of the ISCO, in contrast with the motion of nonspinning particles, where the ISCO is the same in both the upper and lower universes. On the other hand, since the dynamical fourmomentum and kinematical fourvelocity of the spinning particle are not always parallel, we also consider a superluminal bound on the particles motion. In the case of circular orbits at the ISCO, we found that the motion of particles with an adimensional spin parameter lower greater than $s=-1.5$ $(1.5)$ is forbidden. The spin interaction becomes important for Kerr black hole orbiting super massive wormholes SMWH., Comment: 17 pages, 22 figures

We present numerical waveforms of gravitational-wave echoes from spinning exotic compact objects (ECOs) that result from binary black hole coalescence. We obtain these echoes by solving the Teukolsky equation for the $\psi_4$ associated with gravitational waves that propagate toward the horizon of a Kerr spacetime, and process the subsequent reflections of the horizon-going wave by the surface of the ECO, which lies right above the Kerr horizon. The trajectories of the infalling objects are modified from Kerr geodesics, such that the gravitational waves propagating toward future null infinity match those from merging black holes with comparable masses. In this way, the corresponding echoes approximate to those from comparable-mass mergers. For boundary conditions at the ECO surface, we adopt recent work using the membrane paradigm, which relates $\psi_0$ associated with the horizon-going wave and $\psi_4$ of the wave that leaves the ECO surface. We obtain $\psi_0$ of the horizon-going wave from $\psi_4$ using the Teukolsky-Starobinsky relation. The echoes we obtain turn out to be significantly weaker than those from previous studies that generate echo waveforms by modeling the ringdown part of binary black hole coalescence waveforms as originating from the past horizon.

The space-borne gravitational wave (GW) detectors, LISA and TAIJI, are planned to be launched in the 2030s. The dual detectors with comparable sensitivities will form a network observing GW with significant advantages. In this work, we investigate the three possible LISA-TAIJI networks for the different location and orientation compositions of LISA orbit ($+60^\circ$ inclination and trailing the Earth by $20^\circ$) and alternative TAIJI orbit configurations including TAIJIp ($+60^\circ$ inclination and leading the Earth by $20^\circ$), TAIJIc ($+60^\circ$ inclination and co-located with LISA), TAIJIm ($-60^\circ$ inclination and leading the Earth by $20^\circ$). In the three LISA-TAIJI configurations, the LISA-TAIJIm network shows the best performance on the sky localization and polarization determination for the massive binary system due to their better complementary antenna pattern, and LISA-TAIJIc could achieve the best cross-correlation and observe the stochastic GW background with an optimal sensitivity., Comment: 12 pages, 6 figures

A waveform model for the eccentric binary black holes named SEOBNRE has been used to analyze the LIGO-Virgo's gravitational wave data by several groups. The accuracy of this model has been validated by comparing it with numerical relativity. However, SEOBNRE is a time-domain model, and the efficiency for generating waveforms is a bottleneck in data analysis. To overcome this disadvantage, we offer a reduced-order surrogate model for eccentric binary black holes based on the SEOBNRE waveforms. This surrogate model (SEOBNRE\_S) can simulate the complete inspiral-merger-ringdown waves with enough accuracy, covering eccentricities from 0 to 0.25 (0.1), and mass ratio from 1:1 to 5:1 (2:1) for nonspinning (spinning) binaries. The speed of waveform generation is accelerated about $10^2 \sim 10^3$ times than the original SEOBNRE model. Therefore SEOBNRE\_S could be helpful in the analysis of LIGO data to find potential eccentricities., Comment: 18pages, 23 figures

The motion of photons around black holes determines the shape of shadow and match the ringdown properties of a perturbed black hole. Observations of shadows and ringdown waveforms will reveal the nature of black holes. In this paper, we study the motion of photons in a general parametrized metric beyond the Kerr hypothesis. We investigated the radius and frequency of the photon circular orbits on the equatorial plane and obtained fitted formula with varied parameters. The Lyapunov exponent which connects to the decay rate of the ringdown amplitude is also calculated. We also analyzed the shape of shadow with full parameters of the generally axisymmetric metric. Our results imply the potential constraint on black hole parameters by combining the Event Horizon Telescope and gravitational wave observations in the future., Comment: 18 pages, 27 figures

Compact objects inspiraling into supermassive black holes, known as extreme-mass-ratio inspirals, are an important source for future space-borne gravitational-wave detectors. When constructing waveform templates, usually the adiabatic approximation is employed to treat the compact object as a test particle for a short duration, and the radiation reaction is reflected in the changes of the constants of motion. However, the mass of the compact object should have contributions to the background. In the present paper, employing the effective-one-body formalism, we analytically calculate the trajectories of a compact object around a massive Kerr black hole with generally three-dimensional orbits and express the fundamental orbital frequencies in explicit forms. In addition, by constructing an approximate "constant" similar to the Carter constant, we transfer the dynamical quantities such as energy, angular momentum, and the "Carter constant" to the semilatus rectum, eccentricity, and orbital inclination with mass-ratio corrections. The linear mass-ratio terms in the formalism may not be sufficient for accurate waveforms, but our analytical method for solving the equations of motion could be useful in various approaches to building waveform models., Comment: 22 pages, 18figures

Two polarization modes of gravitational wave are derived from the general relativity which are plus and cross modes. However, the alternative theories of gravity can yield the gravitational wave with up to six polarizations. Searching for the polarizations beyond plus and cross is an important test of general relativity. In principle, one space-borne detector, like LISA, could measure the gravitational wave polarizations from a long time observation with its orbital motion. With the comparable sensitivities, the joint LISA and TAIJI missions will improve the observations on the polarization predictions of theories beyond general relativity. In this work, a class of parameterized post-Einsteinian waveform is employed to describe the alternative polarizations, and six parameterized post-Einsteinian parameters quantifying from general relativity waveform are examined by using the LISA-TAIJI network. Our results show that the measurements on amplitudes of alternative polarizations from joint LISA-TAIJI observation could be improved by more than 10 times compared to LISA single mission in an optimal scenario., Comment: 16 pages, 9 figures, accepted for publication in PRD

We introduce a generic algorithm to determine the time delays and spacecraft (S/C) positions to compose any time-delay interferometry (TDI) channel in the dynamical case and evaluate its sensitivity by using a full numerical method. We select 11 second-generation TDI channels constructed from four approaches and investigate their gravitational wave responses, noise levels, and averaged sensitivities under a numerical LISA orbit. The sensitivities of selected channels are various especially for frequencies lower than 20 mHz. The optimal channel A$_2$ (or equivalently E$_2$) combined from second-generation Michelson TDI channels (X$_1$, X$_2$, and X$_3$) achieves the best sensitivity among the channels, while the Sagnac $\alpha_1$ channel shows the worse sensitivity. Multiple channels show better sensitivities at some characteristic frequencies compared to the fiducial X$_1$ channel. The joint $\mathrm{A_2+E_2+T_2}$ observation not only enhances the sensitivity of the X$_1$ channel by a factor of $\sqrt{2}$ to 2 but also improves the capacity of sky coverage., Comment: 13 pages, 8 figures

In this paper we have investigated the dynamics of neutral, electrically charged and magnetized particles around renormalized group improved (RGI) Schwarzschild black hole in the presence of external asymptotically uniform magnetic field. We have analyzed the spacetime structure around RGI black hole by investigating Ricci, the square of Ricci tensor and Kretschmann curvature scalars and shown that only in the case when the parameter $\gamma=0$ the curvature becomes infinite at the center of the black hole, while for non-zero values of $\gamma$ parameter the black hole curvature reflects the properties of regular black hole. Analyzing the innermost stable circular orbits of test neutral particles around RGI black hole and comparing with the results for rotating Kerr black hole we have shown that RGI black hole parameters can mimic the rotation parameter of Kerr black hole upto $a/M \lesssim 0.31$ providing the same ISCO radius. Since according to the astronomical observations of the accretion disks confirm that the astrophysical black holes are rapidly rotating with the spin parameter upto $a/M \sim 0.99$ one may conclude that the effects of parameters of RGI Schwarzschild black hole on the circular orbits of the neutral particles can not mimic the Kerr black hole. Then the Hamilton-Jacobi equation has been used to analyze the charged and magnetized particles motion near the RGI black hole in the presence of the strong interaction between external asymptotically uniform magnetic (electromagnetic) field and magnetized (electrically charged) particle. We have shown that RGI black hole parameters quantitatively change the dynamics of the charged and magnetized particles, in particular ISCO radius of the particles decreases with increasing the parameter $\lambda$, while the increase of the parameter $\gamma$ causes to increase of it., Comment: 16 pages, 16 figures. arXiv admin note: text overlap with arXiv:2010.12863

This work is devoted to study the effects of Einstein-\AE ther gravity on the dynamics of magnetized particles orbiting a static, spherically symmetric and uncharged black hole immersed in an external asymptotically uniform magnetic field in both comoving and proper observers frames. The analysis is carried out by varying the free parameters $c_{13}$ and $c_{14}$ of the Einstein-\AE ther theory and noticing their impacts on the particle trajectories, radii of the innermost stable circular orbits (ISCOs), and the amount of center-of-mass energy produced as a result of the collision. The strength of the magnetic field and the location of circular orbits is significantly affected by varying the above free parameters. We have also made detailed comparisons between the effects of parameters of Einstein-\AE ther and spin of rotating Kerr black holes on ISCO followed by magnetized particles and noticed that both black holes depict similar behaviour for suitable values of $c_{13}$, $c_{14}$, spin and the magnetic coupling parameters which provide exactly the same values for the ISCO. Finally, we have analysed the cases when a static \AE ther black hole can be described as Schwarzschild black hole in modified gravity (MOG) with the corresponding values of the parameters of the black holes., Comment: 17 pages, to appear in Nuclear Physics B

Two recent papers\citep{xmri1, xmri2} revealed that in our Galaxy there are very extreme-mass-ratio inspirals composed by brown dwarfs and the supermassive black hole at the center of the Galaxy. The event rates estimated in these papers are very considerable for future space-borne detectors. In addition, there are plunge events during the formation of inspiraling orbits. In this work, we calculate the gravitational waves from compact objects (brown dwarf, primordial black hole and etc.) plunging into or being scattered by the central supermassive black hole. We find that for space-borne detectors the signal-to-noise ratios of these bursts are quite high. The event rates are estimated as $\sim$ $0.01 {\rm{yr}^{-1}}$ for the Galaxy. If we are lucky, this kind of very extreme-mass-ratio bursts will offer a unique chance to reveal the nearest supermassive black hole and nuclei dynamics. The event rate can be as large as 4 $\sim$ 8 ${\rm yr^{-1}}$ in 10 Mpc, and because the signal is strong enough for observations by space-borne detectors, we have a good chance of being able to probe the nature of neighboring black holes., Comment: 4 pages, 11 figures, 1 table

LISA is considered to be launched alongside the Athena to probe the energetic astrophysical processes. LISA can determine the direction of sources for Athena's follow-up observation. As another space gravitational wave mission, TAIJI is expected to be launched in the 2030s. The LISA-TAIJI network would provide abundant merits for sources understanding. In this work, we simulate the joint LISA-TAIJI observations for gravitational waves from coalescing supermassive black hole binaries and monochromatic sources. By using the numerical mission orbits, we evaluate the performances of sky localization for various time-delay interferometry channels. For 30 days observation until coalescence, the LISA-TAIJI network in optimal operation can localize all simulated binary sources, $(10^7,\ 3.3 \times 10^6)\ M_\odot$, $(10^6,\ 3.3 \times 10^5)\ M_\odot$ and $(10^5,\ 3.3 \times 10^4)\ M_\odot$ at redshift $z=2$, in 0.4 deg$^2$ (field of view of Wide Field Imager on Athena). The angular resolution can be improved by more than 10 times comparing to LISA or TAIJI single detector at a given percentage of population. The improvements for monochromatic sources at 3 mHz and 10 mHz are relatively moderate in one-year observation. The precision of sky localization could be improved by around 1 to 3 times comparing to single LISA at a given percentage of sources. For a simulated 90 days observation for monochromatic waves, the LISA-TAIJI network still represents a considerable localization advantage which could be more than 10 times better., Comment: 18 pages, 12 figures; accepted for publication in PRD

In the first Gravitational-Wave Transient Catalogue of LIGO and Virgo, all events are announced having zero eccentricity. In the present paper, we investigate the performance of SEOBNRE which is a spin-aligned eccentric waveform model in time-domain. By comparing with all the eccentric waveforms in SXS library, we find that the SEOBNRE coincides perfectly with numerical relativity data. Employing the SEOBNRE, we re-estimate the eccentricities of all black hole merger events. We find that most of these events allow a possibility for existence of initial eccentricities at 10 Hz band, but are totally circularized at the observed frequency ($ \gtrsim 20$ Hz). The upcoming update of LIGO and the next generation detector like as Einstein Telescope, will observe the gravitational waves starting at 10 Hz or even lower. If the eccentricity exists at the lower frequency, it may significantly support the dynamical formation mechanism taking place in globular clusters., Comment: 9 pages, 6 figures, 3 tables

Extreme-mass-ratio-inspiral (EMRI) is one of the most important sources for the future space-borne gravitational wave detectors. In such kind of systems, the compact objects usually orbit around the central supermassive black holes with complicated trajectories. Usually, the trajectory is approximated as geodesic of a test-particle in Kerr space-time, and the orbital evolution are simulated with the help of adiabatic approximation. However, this omits the influence of the compact object on the back ground. In the present paper, employing effective-one-body formalism, we analytically calculate out the trajectories of a compact object around a massive Kerr black hole in equatorial-eccentric orbit, and express the fundamental orbital frequencies in explicit forms. Our formalism include the first-order corrections of mass-ratio in the conservative orbital motion. Furthermore, we insert the mass-ratio related terms in the first post-Newtonian energy fluxes. By calculating the gravitational waves from the Teukolsky equations, we quantitatively reveal the influence of the mass of the compact object on the data analysis. We find that the shrinking of geodesic motion by taking the small objects as test particles may be not appropriate for the detection of EMRIs., Comment: 20 pages, 11 figures

The weak equivalence principle (WEP) is the cornerstone of gravitational theories. At the local scale, WEP has been tested to high accuracy by various experiments. On the intergalactic distance scale, WEP could be tested by comparing the arrival time of different messengers emitted from the same source. The gravitational time delay caused by massive galaxies is proportional to $\gamma+1$, where the parameter $\gamma$ is unity in general relativity. The values of $\gamma$ for different massless particles should be different if WEP is violated, i.e., $\Delta \gamma$ is used to indicate the deviation from WEP. So far, $|\Delta \gamma|$ has been constrained with gamma-ray bursts, fast radio bursts, etc. Here we report a new constraint of $|\Delta \gamma|$ by using the gravitational wave data of binary black hole coalescences in the LIGO-Virgo catalogue GWTC-1. The best constraints imply that $|\Delta \gamma| \lesssim 10^{-15}$ at 90 per cent confidence level., Comment: 14 pages, 3 figures

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 dephasing of waveforms compared with general relativity. This kind of dispersion phenomena related with extreme-mass-ratio inspirals could be observed by space-borne detectors, and the constraint on the graviton mass could be improved . Moreover, we find that the dispersion effect may also be constrained by ground detectors better than the current result if a highly eccentric intermediate-mass-ratio inspirals be observed., Comment: 15 pages, 7 figures

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($|\delta_i|<1$) can be discerned only when spin parameter is high. In most cases, the EMRI waveforms related with a non-Kerr metric can be mimicked by the waveform templates produced with a Kerr black hole., Comment: 25 pages, 22 figures