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In the typical data analysis and waveform modelling of the gravitational waves (GWs) signals for binary black holes (BBHs), it's assumed to be isolate sources in the vacuum within the theory of general relativity (GR). However, various kinds of matters may exist around the source or on the path to the detector, and there also exist many different kinds of modified theories of gravity. The effects of these modifications can be characterized within the parameterized post-Einstein (ppE) framework, and the corresponding phase corrections on the waveform at leading post-Newtonian (PN) order are also expressed by the additional parameters for these effects. In this work, we consider the varying-G theory and the dynamical friction of the dark matter spike as an example. Both of these two effects will modify the waveform at -4PN order, if we choose the suitable power law index for the spike. We choose to use a statistic to characterize the dispersion between the posterior of $\dot G$ for different events. For different astronomical models, we find that this statistic can distinguish these two models very effectively. This result indicates that we could use this statistic to distinguish other degenerate effects with the detection of multiple sources., Comment: 9 pages,10 figures

Space-based gravitational wave detectors have the capability to detect signals from very high redshifts. It is interesting to know if such capability can be used to study the global structure of the cosmic space. In this paper, we focus on one particular question: if there exists a reflective cosmic boundary at the high redshift ($z>15$), is it possible to find it? We find that, with the current level of technology: 1) gravitational waves appear to be the only means with which that signatures from the cosmic boundary can possibly be detected; 2) a large variety of black holes, with masses roughly in the range $(10^3\sim 10^6) {\rm~M_\odot}$, can be used for the task; 3) in the presumably rare but physically possible case that two merger events from the growth history of a massive black hole are detected coincidentally, a detector network like TianQin+LISA is essential in help improving the chance to determine the orientation of the cosmic boundary; 4) the possibility to prove or disprove the presence of the cosmic boundary largely depends on how likely one can detect multiple pairs of coincident gravitational wave events., Comment: 11 pages, 6 figures

The opening of the gravitational wave window has significantly enhanced our capacity to explore the universe's most extreme and dynamic sector. In the mHz frequency range, a diverse range of compact objects, from the most massive black holes at the farthest reaches of the Universe to the lightest white dwarfs in our cosmic backyard, generate a complex and dynamic symphony of gravitational wave signals. Once recorded by gravitational wave detectors, these unique fingerprints have the potential to decipher the birth and growth of cosmic structures over a wide range of scales, from stellar binaries and stellar clusters to galaxies and large-scale structures. The TianQin space-borne gravitational wave mission is scheduled for launch in the 2030s, with an operational lifespan of five years. It will facilitate pivotal insights into the history of our universe. This document presents a concise overview of the detectable sources of TianQin, outlining their characteristics, the challenges they present, and the expected impact of the TianQin observatory on our understanding of them., Comment: TianQin Gravitational Wave Whitepaper, 72 pages, 30 figures

The detection of quasi-normal modes during the ringdown phase is a crucial method for testing the no-hair theorem. In this paper, the detectability and resolvability of multiple quasi-normal modes using space-based gravitational wave detectors have been analyzed. The results indicate that TianQin and LISA have the potential to detect and resolve a series of modes, including six fundamental modes, one overtone, and two nonlinear second-order modes. Furthermore, the analysis of systematic errors in the waveform suggests that even modes such as (3,3,1) and (4,3,0), which are unlikely to be directly detected and resolved, need to be taken into account in the ringdown waveform templates., Comment: 13 pages, 7 figures, 1 table

The Einstein-dilaton-Gauss-Bonnet (EdGB) theory is a modified theory which include a scalar field to couple with the higher order curvature terms. It has already been constrained with various observations include the gravitational wave (GW) with LIGO, Virgo and KAGRA (LVK) Collaboration. In this work, we study the problem of using the GW of Extreme Mass-Ratio Inspiral (EMRI) to constrain the EdGB theory. We use the "numerical kludge (NK)" method to construct the waveform of EMRI in the EdGB theory, focusing on the case when the central black hole is spinless. We then study how a future space-borne gravitational wave detector, TianQin, for example, can place constraints on the EdGB theory through the detection of EMRIs. With the analysis using mismatch and Fisher Information Matrix (FM), we find that the EdGB parameter $\sqrt{\alpha}$ is expected to be constrained to the level of $\sim\mathcal{O}(0.1)$ km., Comment: 9 page, 3 figures

The direct detection of gravitational waves offers a powerful tool to explore the nature of gravity and the structure of space-time. This paper focuses on the capabilities of space-based gravitational wave detectors in testing space-time non-commutativity. Our findings indicate that TianQin has the potential to impose constraints on the non-commutative scale at a sub-Planckian level using massive black hole binaries. Additionally, we have developed a pipeline tailored to this specific topic., Comment: 9 Pages, 5 figures

This paper analyses the impact of various parameter changes on the estimation of parameters for massive black hole binary (MBHB) systems using a Bayesian inference technique. Several designed MBHB systems were chosen for comparison with a fiducial system to explore the influence of parameters such as sky location, inclination angle, anti-spin, large mass ratio and light mass. And the two reported MBHB candidates named OJ287 and Tick-Tock are also considered. The study found that the network of TianQin and LISA can break certain degeneracies among different parameters, improving the estimation of parameters, particularly for extrinsic parameters. Meanwhile, the degeneracies between different intrinsic parameters are highly sensitive to the value of the parameters. Additionally, the small inclination angles and limited detection of the inspiral phase can introduce significant bias in the estimation of parameters. The presence of instrument noise will also introduce bias and worsen the precision. The paper concludes that the network of TianQin and LISA can significantly improve the estimation of extrinsic parameters by about one order of magnitude while yielding slight improvements in the intrinsic parameters. Moreover, parameter estimation can still be subject to biases even with a sufficiently high signal-to-noise ratio if the detected signal does not encompass all stages of the inspiral, merger, and ringdown., Comment: 17 pages, 10 figures

The memory effect in gravitational waves is a direct prediction of general relativity. The presence of the memory effect in gravitational wave signals not only serves as a test for general relativity but also establishes connections between soft theorem, and asymptotic symmetries, serving as a bridge for exploring fundamental physics. Furthermore, with the ongoing progress in space-based gravitational wave detection projects, the gravitational wave memory effect generated by the merger of massive binary black hole binaries is becoming increasingly significant and cannot be ignored. In this work, we perform the full Bayesian analysis of the gravitational wave memory effect with TianQin. The results indicate that the memory effect has a certain impact on parameter estimation but does not deviate beyond the 1$\sigma$ range. Additionally, the Bayes factor analysis suggests that when the signal-to-noise ratio of the memory effect in TianQin is approximately 2.36, the $\text{log}_{10}$ Bayes factor reaches 8. This result is consistent with the findings obtained from a previous mismatch threshold.

This paper describes a method that seeks to find the fully separated wave equations for all the metric components over the Kerr background directly. Unfortunately, the solution found in the original version is purely gauge. The main text has not been corrected, as a follow up updated is hoped for and the correct solution is still being searched with the method., Comment: 5 pages; v2: Abstract tempararily modified to reflect a fatal flaw in the paper

Space-based gravitational wave detectors such as TianQin, LISA, and TaiJi have the potential to outperform themselves through joint observation. To achieve this, it is desirable to practice joint data analysis in advance on simulated data that encodes the intrinsic correlation among the signals found in different detectors that operate simultaneously. In this paper, we introduce \texttt{GWSpace}, a package that can simulate the joint detection data from TianQin, LISA, and TaiJi. The software is not a groundbreaking work that starts from scratch. Rather, we use as many open-source resources as possible, tailoring them to the needs of simulating the multi-mission science data and putting everything into a ready-to-go and easy-to-use package. We shall describe the main components, the construction, and a few examples of application of the package. A common coordinate system, namely the Solar System Barycenter (SSB) coordinate system, is utilized to calculate spacecraft orbits for all three missions. The paper also provides a brief derivation of the detection process and outlines the general waveform of sources detectable by these detectors., Comment: 24 pages, 13 figures, GWSpace will be uploaded at https://github.com/TianQinSYSU/GWSpace

TianQin and LISA are space-based laser interferometer gravitational wave (GW) detectors planned to be launched in the mid-2030s. Both detectors will detect low-frequency GWs around $10^{-2}\,{\rm Hz}$, however, TianQin is more sensitive to frequencies above this common sweet-spot while LISA is more sensitive to frequencies below $10^{-2}\,{\rm Hz}$. Therefore, TianQin and LISA will be able to detect the same sources but with different accuracy depending on the source and its parameters. We consider some of the most important astrophysical sources -- massive black hole binaries, stellar-mass black hole binaries, double white dwarfs, extreme mass ratio inspirals, light and heavy intermediate mass ratio inspirals, as well as the stochastic gravitational background of astrophysical origin -- that TianQin and LISA will be able to detect. For each of these sources, we analyze how far they can be detected (detection distance) and how well their parameters can be measured (detection accuracy) using a Fisher Matrix analysis. We compare the results obtained by the three detection scenarios (TianQin alone, LISA alone, and joint detection by LISA and TianQin) highlighting the gains from joint detection as well as the contribution of TianQin and LISA to a combined study of astrophysical sources. In particular, we consider the different orientations, lifetimes, and duty cycles of the two detectors to explore how they can give a more complete picture when working together., Comment: 49 pages, 63 figures

In this paper, we revisit the problem of using gravitational wave data to test the Einstein-dilation-Gauss-Bonnet theory, by using nine selected gravitational wave events from GWTC-3. Compared with existing work, we are taking into account the higher harmonics more properly and we also study the contribution of the merger-ringdown data. Using the inspiral data alone, we find that the best result is from GW200115, giving $\sqrt{|\alpha|} < 1.1$ km, which is about 17\% tighter than the previous best result. We also notice the possible existence of a simple unexpected relation among the constraints from different events. Several combinations of the selected events give $\sqrt{|\alpha|} \leq 1.0$ km. The result is further improved when the merger-ringdown data is also included, using two phenomenological schemes, giving $\sqrt{|\alpha|} < 0.87$ km for GW200115 in the best case scenario.

In this paper, we carry out a systematic study of the prospect of testing general relativity with the inspiral signals of black hole binaries that could be detected with TianQin. The study is based on the parameterized post-Einsteinian (ppE) waveform, so that many modified gravity theories can be covered simultaneously. We consider black hole binaries with total masses ranging from $10\rm M_\odot\sim10^7 M_\odot$ and ppE corrections at post-Newtonian (PN) orders ranging from $-4$PN to $2$PN. Compared to the current ground-based detectors, TianQin can improve the constraints on the ppE phase parameter $\beta$ by orders of magnitude. For example, the improvement at the $-4$PN and $2$PN orders can be about $13$ and $3$ orders of magnitude (compared to the results from GW150914), respectively. Compared to future ground-based detectors, such as ET, TianQin is expected to be superior below the $-1$PN order, and for corrections above the $-0.5$PN order, TianQin is still competitive near the large mass end of the low mass range $[10 \rm M_\odot, \,10^3 \rm M_\odot]\,$. Compared to the future space-based detector LISA, TianQin can be competitive in the lower mass end as the PN order is increased. For example, at the $-4$PN order, LISA is always superior for sources more massive than about $30\rm M_\odot\,$, while at the $2$PN order, TianQin becomes competitive for sources less massive than about $10^4\rm M_\odot$. We also study the scientific potentials of detector networks involving TianQin, LISA and ET, and discuss the constraints on specific theories such as the dynamic Chern-Simons theory and the Einstein-dilaton Gauss-Bonnet theory.

It is easy to reason that gravity might be the effect of a fluid in disguise, as it will naturally arise in emergent gravity models where gravity is due to the effect of some fundamental particles, with the latter expected to behave collectively like a fluid at the macroscopic scale. We call this the fluid/gravity equivalence. The key difficulty with the fluid/gravity equivalence is to find the correct metric-fluid relation (the relation between the emergent metric and the fluid properties) so that the fluid not only has physically acceptable properties but also obeys the usual hydrodynamic equations, while at the same time the emergent metric also obeys the Einstein equations. Faced with the problem, we have previously made a tentative proposal of the metric-fluid relation, focusing only on obtaining physically acceptable predictions on the fluid properties. In this paper, however, we find that for the general gravitational wave spacetime near the null infinity, the underlying fluid not only has physically acceptable properties, but also satisfies the expected relativistic hydrodynamic equations in the Minkowski background, thus providing a concrete example satisfying both of the major requirements expected for the fluid/gravity equivalence., Comment: published version

The detection of stochastic gravitational wave background (SGWB) is among the leading scientific goals of the space-borne gravitational wave observatory, which would have significant impact on astrophysics and fundamental physics. In this work, we developed a data analysis software, \texttt{TQSGWB}, which can extract isotropic SGWB using the Bayes analysis method based on the TianQin detector. We find that for the noise cross spectrum, there are imaginary components and they play an important role in breaking the degeneracy of the position noise in the common laser link. When the imaginary corrections are considered, the credible regions of the position noise parameters are reduced by two orders of magnitude. We demonstrate that the parameters of various signals and instrumental noise could be estimated directly in the absence of a Galactic confusion foreground through Markov chain Monte Carlo sampling. With only a three-month observation, we find that TianQin could be able to confidently detect SGWBs with energy density as low as $\Omega_{\rm PL} = 1.3 \times 10^{-12}$, $\Omega_{\rm Flat} = 6.0 \times 10^{-12}$, and $\Omega_{\rm SP} = 9.0 \times 10^{-12}$, for power-law, flat, and single-peak models respectively., Comment: 28 pages, 8 figures

The detection of gravitational wave (GW) has opened a new window to test the theory of gravity in the strong field regime. In general relativity (GR), GW can only possess two tensor polarization modes, which are known as the $+$ and $\times$ modes. However, vector and scalar modes can exist in some modified theories of gravity, and we can test the gravitational theories by probing these extra polarization modes. As a space-borne GW detector, TianQin will be launched in the 2030s, and it is expected to observe plenty of GW signals, including those from nearly ten-thousands double white dwarfs (DWDs) in our galaxy. This offers an excellent chance for testing the existence of extra polarization modes. In this article, we analyze the capability of detecting the extra polarization modes with DWDs. For the extra modes, we consider both the leading order dipole radiation and the subleading quadrupole radiation. We find that the capability of TianQin has very strong dependency on the source orientation. We also analyze all the verification binaries with determined position and frequency, and find that ZTF J1539 can give the best constraint on the extra polarization modes. We have also considered the case of TianQin twin constellation, and the joint observation with LISA., Comment: 13 pages, 18 figures, 5 tables, matches the published version

The gravitational wave memory effect is a prediction of general relativity. The presence of memory effect in gravitational wave signals not only provides the chance to test an important aspect of general relativity, but also represents a potentially non-negligible contribution to the waveform for certain gravitational wave events. In this paper, we study the prospect of detecting the gravitational wave memory effect directly with the planned space-based gravitational wave detector -- TianQin. We find that during its 5 years operation, for the gravitational wave signals that could be detected by TianQin, about $0.5\sim2.0$ signals may contain displacement memory effect with signal-to-noise ratios (SNRs) greater than 3. This suggests that the chance for TianQin to detect the displacement memory effect directly is low but not fully negligible. In contrast, the chance to detect the spin memory is negligible. We also study that in which parameter space, the memory effect is expected to be significant in waveform modeling., Comment: 14 pages, 9 figures

The space-borne gravitational wave detectors will observe a large population of double white dwarf binaries in the Milky Way. However, the search for double white dwarfs in the gravitational wave data will be time-consuming due to the large number of templates involved and antenna response calculation. In this paper, we implement an iterative combinatorial algorithm to search for double white dwarfs in MLDC-3.1 data. To quickly determine the rough parameters of the target sources, the following algorithms are adopted in a coarse search process: (1) using the downsampling method to reduce the number of original data points; (2) using the undersampling method to speed up the generation of a single waveform template; (3) using the stochastic template bank method to quickly construct the waveform template bank while achieving high coverage of the parameter space; (4) Combining the FFT acceleration algorithm with the stochastic template bank to reduce the calculation time of a single template. A fine search process is applied to further determine the parameters of the signals based on the coarse search, for which we adopt the particle swarm optimization. Finally, we detected $\mathcal{O}(10^4)$ double white dwarf signals, validating the feasibility of our method., Comment: 16 pages, 15 figures

Gravitational wave signal from the inspiral of stellar-mass binary black hole can be used as standard sirens to perform cosmological inference. This inspiral covers a wide range of frequency bands, from the millihertz band to the audio-band, allowing for detections by both space-borne and ground-based gravitational wave detectors. In this work, we conduct a comprehensive study on the ability to constrain the Hubble constant using the dark standard sirens, or gravitational wave events that lack electromagnetic counterparts. To acquire the redshift information, we weight the galaxies within the localization error box with photometric information from several bands and use them as a proxy for the binary black hole redshift. We discover that TianQin is expected to constrain the Hubble constant to a precision of roughly $30\%$ through detections of $10$ gravitational wave events; in the most optimistic case, the Hubble constant can be constrained to a precision of $< 10 \%$, assuming TianQin I+II. In the optimistic case, the multi-detector network of TianQin and LISA is capable of constraining the Hubble constant to within $5\%$ precision. It is worth highlighting that the multi-band network of TianQin and Einstein Telescope is capable of constraining the Hubble constant to a precision of about $1\%$. We conclude that inferring the Hubble constant without bias from photo-z galaxy catalog is achievable, and we also demonstrate self-consistency using the P$-$P plot. On the other hand, high-quality spectroscopic redshift information is crucial for improving the estimation precision of Hubble constant., Comment: 29 pages, 14 figures, update to match published version

In this work, we study the prospect of detecting the stochastic gravitational-wave background with the TianQin Observatory. We consider sources of both astrophysical-origin and cosmological-origin, including stellar-mass binary black holes, binary neutron stars, Galactic white dwarves, inflation, first-order phase transitions, and cosmic defects. For the detector configurations, we consider TianQin, TianQin I+II, and TianQin + LISA. We study the detectability of stochastic gravitational-wave backgrounds with both the cross correlation and null channel methods, and present the corresponding power-law integrated sensitivity curves. We introduce the definition of the "joint foreground" with a network of detectors. With the joint foreground, the number of resolved double white dwarves in the Galaxy will be increased by 5$-$22\% compared with a simple combination of individual detectors. The astrophysical background is expected to be detectable with a signal-to-noise ratio of 100 after 5 years of operation and dominated by the extragalactic double white dwarves. On the other hand, due to the uncertain nature of underlying models, we can only estimate the detection capability of the cosmological background for specific cases., Comment: 20 pages, 10 figures, update to match published version

Space-borne gravitational wave detectors like TianQin are expected to detect GW signals emitted by the mergers of massive black hole binaries. Luminosity distance information can be obtained from GW observations, and one can perform cosmological inference if redshift information can also be extracted, which would be straightforward if an electromagnetic counterpart exists. In this paper, we concentrate on the conservative scenario where the EM counterparts are not available, and comprehensively study if cosmological parameters can be inferred through a statistical approach, utilizing the non-uniform distribution of galaxies as well as the black hole mass-host galaxy bulge luminosity relationship. By adopting different massive black hole binary merger models, and assuming different detector configurations, we conclude that the statistical inference of cosmological parameters is indeed possible. TianQin is expected to constrain the Hubble constant to a relative error of about 4%-7%, depending on the underlying model. The multidetector network of TianQin and LISA can significantly improve the precision of cosmological parameters. In the most favorable model, it is possible to achieve a level of 1.7% with a network of TianQin and LISA. We find that without EM counterparts, constraints on all other parameters need a larger number of events or more precise sky localization of GW sources, which can be achieved by the multidetector network or under a favorable model for massive black hole mergers. However, in the optimistic case, where EM counterparts are available, one can obtain useful constraints on all cosmological parameters in the Lambda-CDM cosmology, regardless of the population model. Moreover, we can also constrain the equation of state of the dark energy without the EM counterparts, and it is even possible to study the evolution of EoS of the DE when the EM counterparts are observed., Comment: 34 pages, 17 figures, update to match published version

Constituted with a massive black hole and a stellar mass compact object, Extreme Mass Ratio Inspiral (EMRI) events hold unique opportunity for the study of massive black holes, such as by measuring and checking the relations among the mass, spin and quadrupole moment of a massive black hole, putting the no-hair theorem to test. TianQin is a planned space-based gravitational wave observatory and EMRI is one of its main types of sources. It is important to estimate the capacity of TianQin on testing the no-hair theorem with EMRIs. In this work, we use the analytic kludge waveform with quadrupole moment corrections and study how the quadrupole moment can be constrained with TianQin. We find that TianQin can measure the dimensionless quadrupole moment parameter with accuracy to the level of $10^{-5}$ under suitable scenarios. The choice of the waveform cutoff is found to have significant effect on the result: if the Schwarzschild cutoff is used, the accuracy depends strongly on the mass of the massive black hole, while the spin has negligible impact; if the Kerr cutoff is used, however, the dependence on the spin is more significant. We have also analyzed the cases when TianQin is observing simultaneously with other detectors such as LISA., Comment: 10 pages, 9 figures, matches the published version

TianQin is a proposed space gravitational-wave detection mission using circular high Earth orbits. The geocentric concept has raised questions about the disturbing effect of the nearby gravity field of the Earth-Moon system on the highly-sensitive intersatellite ranging measurements. Here we examine the issue through high precision numerical orbit simulation with detailed gravity-field models. By evaluating range accelerations between distant free-falling test masses, the study shows that the majority of the Earth-Moon's gravity disturbances are not in TianQin's detection frequency band above $10^{-4}$ Hz, and hence present no showstoppers to the mission., Comment: 7 pages, 4 figures, to match the accepted version by Phys. Rev. D

TianQin is a geocentric space-based gravitational-wave observatory mission consisting of three drag-free controlled satellites in an equilateral triangle with an orbital radius of $ 10^{5}$ km. The constellation faces the white-dwarf binary RX J0806.3+1527 located slightly below the ecliptic plane, and is subject to gravitational perturbations that can distort the formation. In this study, we present combined methods to optimize the TianQin orbits so that a set of 5-year stability requirements can be met. Moreover, we discuss slow long-term drift of the detector pointing due to orbital precession, and put forward stable orbits with six other pointings along the lunar orbital plane. Some implications of the findings are pointed out.

TianQin is a planned space-based gravitational wave (GW) observatory consisting of three earth orbiting satellites with an orbital radius of about $10^5~{\rm km}$. The satellites will form a equilateral triangle constellation the plane of which is nearly perpendicular to the ecliptic plane. TianQin aims to detect GWs between $10^{-4}~{\rm Hz}$ and $1~{\rm Hz}$ that can be generated by a wide variety of important astrophysical and cosmological sources, including the inspiral of Galactic ultra-compact binaries, the inspiral of stellar-mass black hole binaries, extreme mass ratio inspirals, the merger of massive black hole binaries, and possibly the energetic processes in the very early universe or exotic sources such as cosmic strings. In order to start science operations around 2035, a roadmap called the 0123 plan is being used to bring the key technologies of TianQin to maturity, supported by the construction of a series of research facilities on the ground. Two major projects of the 0123 plan are being carried out. In this process, the team has created a new generation $17~{\rm cm}$ single-body hollow corner-cube retro-reflector which has been launched with the QueQiao satellite on 21 May 2018; a new laser ranging station equipped with a $1.2~{\rm m}$ telescope has been constructed and the station has successfully ranged to all the five retro-reflectors on the Moon; and the TianQin-1 experimental satellite has been launched on 20 December 2019 and the first round result shows that the satellite has exceeded all of its mission requirements., Comment: 16 pages, 1 figure, invited article to a special section in PTEP

The TianQin-1 satellite (TQ-1), which is the first technology demonstration satellite for the TianQin project, was launched on 20 December 2019. The first round of experiment had been carried out from 21 December 2019 until 1 April 2020. The residual acceleration of the satellite is found to be about $1\times10^{-10}~{\rm m}/{\rm s}^{2}/{\rm Hz}^{1/2}$ at $0.1~{\rm Hz}\,$ and about $5\times10^{-11}~{\rm m}/{\rm s}^{2}/{\rm Hz}^{1/2}$ at $0.05~{\rm Hz}\,$, measured by an inertial sensor with a sensitivity of $5\times10^{-12}~{\rm m}/{\rm s}^{2}/{\rm Hz}^{1/2}$ at $0.1~{\rm Hz}\,$. The micro-Newton thrusters has demonstrated a thrust resolution of $0.1~\mu{\rm N}$ and a thrust noise of $0.3~\mu{\rm N}/{\rm Hz}^{1/2}$ at $0.1~{\rm Hz}$. The residual noise of the satellite with drag-free control is $3\times10^{-9}~{\rm m}/{\rm s}^{2}/{\rm Hz}^{1/2}$ at $0.1~{\rm Hz}\,$. The noise level of the optical readout system is about $30~{\rm pm}/{\rm Hz}^{1/2}$ at $0.1~{\rm Hz}\,$. The temperature stability at temperature monitoring position is controlled to be about $\pm3~{\rm mK}$ per orbit, and the mismatch between the center-of-mass of the satellite and that of the test mass is measured with a precision of better than $0.1~{\rm mm}$., Comment: 17 pages, 11 figures

Systems consisting of a massive black hole and a stellar-origin compact object (CO), known as extreme-mass-ratio inspirals (EMRIs), are of great significance for space-based gravitational-wave detectors, as they will allow for testing gravitational theories in the strong field regime, and for checking the validity of the black hole no-hair theorem. In this work, we present a calculation of the EMRI rate and parameter estimation capabilities of the TianQin observatory, for various astrophysical models for these sources. We find that TianQin can observe EMRIs involving COs with mass of 10$M_\odot$ up to redshift $\sim2$. We also find that detections could reach tens or hundreds per year in the most optimistic astrophysical scenarios. Intrinsic parameters are expected to be recovered to within fractional errors of $\sim 10^{-6}$, while typical errors on the luminosity distance and sky localization are 10% and 10 deg$^2$, respectively. TianQin observation of EMRIs can also constrain possible deviations from the Kerr quadrupole moment to within fractional errors $\lesssim10^{-4}$. We also find that a network of multiple detectors would allow for improvements in both detection rates (by a factor $\sim 1.5$ -$3$) and in parameter estimation precision (20-fold improvement for the sky localization and fivefold improvement for the other parameters)., Comment: 13 pages, 5 figures

We explore the prospects of detecting of Galactic double white dwarf (DWD) binaries with the space-based gravitational wave (GW) observatory TianQin. In this work, we analyze both a sample of currently known DWDs and a realistic synthetic population of DWDs to assess the number of guaranteed detections and the full capacity of the mission. We find that TianQin can detect 12 out of $\sim100$ known DWDs; GW signals of these binaries can be modeled in detail ahead of the mission launch, and therefore they can be used as verification sources. Besides we estimate that TianQin has potential to detect as many as $10^4$ DWDs in the Milky Way. TianQin is expected to measure their orbital periods and amplitudes with accuracies of $\sim10^{-7}$ and $\sim0.2$, respectively, and to localize on the sky a large fraction (39%) of the detected population to better than 1 deg$^2$. We conclude that TianQin has the potential to significantly advance our knowledge on Galactic DWDs by increasing the sample up to 2 orders of magnitude, and will allow their multi-messenger studies in combination with electromagnetic telescopes. We also test the possibilities of different configurations of TianQin: (1) the same mission with a different orientation, (2) two perpendicular constellations combined into a network, and (3) the combination of the network with the ESA-led Laser Interferometer Space Antenna. We find that the network of detectors boosts the accuracy on the measurement of source parameters by 1-2 orders of magnitude, with the improvement on sky localization being the most significant., Comment: 21 pages, 7 figures, 6 tables, 5 appendices, to be published in Phys. Rev. D

We study the prospect of using TianQin to detect stellar-mass binary black holes (SBBHs). We estimate the expected detection number as well as the precision of parameter estimation on SBBH inspirals, using five different population models. We note TianQin can possibly detect a few SBBH inspirals with signal to noise ratios greater than 12; lowering the threshold and combining multiple detectors can both boost the detection number. The source parameters can be recovered with good precision for most events above the detection threshold. For example, the precision of the merger time most likely occurs near 1s, making it possible to guide the detection of the ground-based detectors, the precision of the eccentricity $e_0$ most likely occurs near $10^{-4}$, making it possible to distinguish the formation channels, and the precision of the mass parameter is better than $10^{-6}$ in general and most likely occurs near $10^{-7}$. We note, in particular, that for a typical merger event, the error volume is likely to be small enough to contain only the host galaxy, which could greatly help in the study of gravitational wave cosmology and relevant studies through the multimessenger observation., Comment: 20 pages, 8 figures, published in Phys. Rev. D

An explicit example is found showing how a modified theory of gravity can be constrained with the ringdown signals from merger of binary black holes. This has been made possible by the fact that the modified gravitational theory considered in this work has an exact rotating black hole solution and that the corresponding quasi-normal modes can be calculated. With these, we obtain the possible constraint that can be placed on the parameter describing the deviation of this particular alternative theory from general relativity by using the detection of the ringdown signals from binary black holes's merger with future space-based gravitational wave detectors., Comment: 7 pages, 4 figures, 4 tables, matches the published version

We study the capability of the space-based gravitational wave observatory TianQin to test the no-hair theorem of General Relativity, using the ringdown signal from the coalescence of massive black hole binaries. We parameterize the ringdown signal by the four strongest quasinormal modes and estimate the signal to noise ratio for various source parameters. We consider constraints both from single detections and from all the events combined throughout the lifetime of the observatory, for different astrophysical models. We find that at the end of the mission, TianQin will have constrained deviations of the frequency and decay time of the dominant 22 mode from the general relativistic predictions to within 0.2% and 1.5% respectively, the frequencies of the subleading modes can be also constrained within 0.3%. We also find that TianQin and LISA are highly complementary, by virtue of their different frequency windows. Indeed, LISA can best perform ringdown tests for black hole masses in excess of $\sim 3\times 10^6 M_\odot$, while TianQin is best suited for lower masses., Comment: 10 pages, 12 figures

We investigate the prospects of detecting gravitational waves from coalescing massive black hole binaries in the Universe with the TianQin observatory, a space-based gravitational wave interferometer proposed to be launched in the 2030s. To frame the scientific scope of the mission, in this paper, we carry out a preliminary estimation of the signal-to-noise ratio, detection rate and parameter estimation precision of massive black hole binaries detectable by TianQin. In order to make our results as robust as possible, we consider several models of the growth history of massive black holes, exploring the effect of some key astrophysical prescriptions as well the impact of the employed computational methods. In the most optimistic model, TianQin can detect as many as approximately 60 mergers per year. If TianQin detects a merger at redshift of 15, it will be capable of estimating its luminosity distance to within an accuracy of 10%; for a nearby event at redshift approximately 2, TianQin can issue early warnings 24 hours before coalescence, with a timing accuracy of around three hours and a sky localization ability of approximately 80 deg$^2$, thus enabling multi-messenger observations., Comment: 17 pages, 6 figures

Hidden conformal symmetries of scalar field on various black hole backgrounds have been investigated for years, but whether those features holds for other fields are still open questions. Recently, with proper assumptions, Lunin achieves to the separation of variables for Maxwell equations on Kerr background. In this paper, with that equation, we find that hidden conformal symmetry appears at near region under low frequency limit. We also extended those results to vector field on Kerr-(A)dS and Kerr-NUT-(A)dS backgrounds, then hidden conformal symmetry also appears if we focusing on the near-horizon region at low frequency limit., Comment: 18 pages, no figure, matches the published version

Recently it has been shown that there is asymptotic BMS-like symmetry associated with the near-horizon geometry of black holes in three and four dimensions. In this paper, we show that the presence of such BMS-like symmetry is a ubiquitous feature for black holes in generic dimensions. For black holes in $D$ dimensions, the symmetry contains 2 supertranslations and $D-2$ generalized superrotations. The superrotations are found to generate a generalized Witt-like algebra that was previously noticed in a rather different construction. In the case of stationary and axisymmetric black holes, we calculate the surface charges and show that the zero-mode charges are intimately related to the entropy and angular momenta of the black hole., Comment: 17 pages, 0 figures

We study in some detail the "extended Kerr-Schild" formulation of general relativity, which decomposes the gauge-independent degrees of freedom of a generic metric into two arbitrary functions and the choice of a flat background tetrad. We recast Einstein's equations and spacetime curvatures in the extended Kerr-Schild form and discuss their properties, illustrated with simple examples., Comment: 12 pages, 0 figures

We derive an ansatz for the five dimensional equal-rotation Kerr-Newman metric that contains two unknown functions. By solving for these functions through perturbation series, we find that the metric can be cast into the Kerr-Shild form in a background that is flat at the spatial infinity., Comment: 13 pages, fixing a loophole in the original version of the paper

TianQin is a proposal for a space-borne detector of gravitational waves in the millihertz frequencies. The experiment relies on a constellation of three drag-free spacecraft orbiting the Earth. Inter-spacecraft laser interferometry is used to monitor the distances between the test masses. The experiment is designed to be capable of detecting a signal with high confidence from a single source of gravitational waves within a few months of observing time. We describe the preliminary mission concept for TianQin, including the candidate source and experimental designs. We present estimates for the major constituents of the experiment's error budget and discuss the project's overall feasibility. Given the current level of technology readiness, we expect TianQin to be flown in the second half of the next decade., Comment: 32 pages, 4 figures, to be published in Class. Quantum Grav

This talk adds more detail to the proposed TianQin mission \cite{TQ}. The response of TianQin to a binary source is an important problem for the experiment. Here we present the detail of the response function of an equal-arm Michelson interferometer to the gravitation waves of a binary source with a circular orbit., Comment: To be published in the proceedings of the "XIIth International Conference on Gravitation, Astrophysics and Cosmology", (Moscow, Russia, 2015), World Scientific, Singapore

For a stationary and axisymmetric black hole, there is a natural way to split the fields into a probe sector and a background sector. The equations of motion for the probe sector enjoy a significantly enhanced symmetry on the black hole horizon. The extended symmetry is conformal in four dimensions, while in higher dimensions it is much bigger. This puts conformal symmetry at the bottom of the ladder of symmetries that can arise on black hole horizons in generic dimensions., Comment: 8 pages

In this paper we treat the black hole horizon as a physical boundary to the spacetime and study its dynamics following from the Gibbons-Hawking-York boundary term. Using the Kerr black hole as an example we derive an effective action that describes, in the large wave number limit, a massless Klein-Gordon field living on the average location of the boundary. Complete solutions can be found in the small rotation limit of the black hole. The formulation suggests that the boundary can be treated in the same way as any other matter contributions. In particular, the angular momentum of the boundary matches exactly with that of the black hole, suggesting an interesting possibility that all charges (including the entropy) of the black hole are carried by the boundary. Using this as input, we derive predictions on the Planck scale properties of the boundary., Comment: References added, nature of boundary stress tensor clarified, discussion of statistics refined and a mistake with Hawking temperature corrected, 16 pages; version to appear in journal

N-point correlation functions of conserved currents and weight-two scalar operators of the three-dimensional free fermion vector model are found as invariants of the higher-spin symmetry in four-dimensional AdS. These are the correlators of the unbroken Vasiliev higher-spin theory. The results extend the recent work arXiv:1210.7963 and are complementary to arXiv:1301.3123 where the correlators were computed entirely on the boundary., Comment: 20 pages, cosmetic changes in (10)

We study conformal symmetries on the horizon of a general stationary and axisymmetric black hole. We find that there exist physically reasonable boundary conditions that uniquely determine a set of symmetry generators, which form one copy of the Virasoro algebra. For extremal black holes, Cardy's formula reproduces exactly the Bekenstein-Hawking entropy., Comment: 17 pages

We suggest a way to study possible conformal symmetries on black hole horizons. We do this by carrying out a Kaluza-Klein like reduction of the Einstein-Hilbert action along the ignorable coordinates of stationary and axisymmetric black holes. Rigid diffeomorphism invariance of the $m$-ignorable coordinates then becomes a global $SL(m,R)$ gauge symmetry of the reduced action. Related to each non-vanishing angular velocity there is a particular $SL(2,R)$ subgroup, which can be extended to the Witt algebra on the black hole horizons. The classical Einstein-Hilbert action thus has $k$-copies of infinite dimensional conformal symmetries on a given black hole horizon, with $k$ being the number of non-vanishing angular velocities of the black hole., Comment: A demonstration of the first law of black hole thermodynamics is added to section 3; and the introduction section is thoroughly revised; 22 pages

In the background of a stationary black hole, the "conserved current" of a particular spinor field always approaches the null Killing vector on the horizon. What's more, when the black hole is asymptotically flat and when the coordinate system is asymptotically static, then the same current also approaches the time Killing vector at the spatial infinity. We test these results against various black hole solutions and no exception is found. The spinor field only needs to satisfy a very general and simple constraint., Comment: 19 pages