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The spatial variation and temporal variation in surface potential are important error sources in various precision experiments and deserved to be considered carefully. In the former case, the theoretical analysis shows that this effect depends on the surface potentials through their spatial autocorrelation functions. By making some modification to the quasi-local correlation model, we obtain a rigorous formula for the patch force, where the magnitude is proportional to ${\frac{1}{{{a}^{2}}}{{(\frac{a}{w})}^{\beta (a/w)+2}}}$ with ${a}$ the distance between two parallel plates, ${w}$ the mean patch size, and ${\beta}$ the scaling coefficient from ${-2}$ to ${-4}$. A torsion balance experiment is then conducted, and obtain a 0.4 mm effective patch size and 20 mV potential variance. In the latter case, we apply an adatom diffusion model to describe this mechanism and predicts a ${f^{-3/4}}$ frequency dependence above 0.01 ${\rm mHz}$. This prediction meets well with a typical experimental results. Finally, we apply these models to analyze the patch effect for two typical experiments. Our analysis will help to investigate the properties of surface potentials.

In the electromagnetic channel, chaotic gravitational lensing is a peculiar phenomenon in strong gravitational lensing. In this work, we analyze the properties and emergence of chaotic gravitational lensing in the Manko-Novikov black hole spacetime. Aiming to understand better the underlying physics, we elaborate on the boundaries of the accessible region in terms of the analyses of the contours of the effective potentials. The latter is associated with the two roots of a quadratic equation. In particular, we explore its interplay with ergoregion, which leads to specific features of the effective potentials, such as the emergence of cuspy edge and the formation of {\it pocket}, that serves as a static constraint on the geodesics. Besides, we investigate the properties of the radial and angular accelerations at the turning points in photons' trajectories. Moreover, the accelerations are analyzed, which is argued to provide a kinematic constraint on the geodesics. It is concluded that the onset of the chaotic lensing is crucially related to both constraints, and as a result, an arbitrarily slight deviation in the incident photon is significantly amplified during the course of evolution through an extensive period, demonstrating the complexity in the highly nonlinear deterministic gravitational system., Comment: 18 pages, 13 figures

The search for dynamically screening the coupling between the scalar field and matter in high-density environment is achievable with the symmetron model. The high-accuracy and short-range gravity experiment is proposed to test the symmetron model. In this Letter, the data of the HUST-2020 torsion pendulum experiment testing the inverse-square law at submillimeter range is analyzed to constrain the symmetron model. The results show that the HUST-2020 experiment is uniquely sensitive to probe the symmetron model with a mass scale of μ=7.2×10^{-3} eV, and the self-coupling parameter λ≲105 is excluded at mass scale M=0.3 TeV. Especially, at the dark energy scale μ=2.4×10^{-3} eV, the constraint at M=1.3 TeV is improved by about 10 times the previous constraints on the torsion pendulum experiment.

The time delay interferometry (TDI) is an algorithm proposed to suppress the laser frequency noise in space-borne gravitational wave detectors. As a post-processing technique, it is implemented by constructing a virtual equal arm interferometer through an appropriate combination of the time-shifted data streams. Such an approach is tailored to the intrinsic feature of the space-based gravitational wave detection, namely, the distances between spacecraft are governed by the orbit dynamics and thus can not be held constant. Among different implementations, the geometric TDI was introduced as a method of exhaustion to evaluate the second-generation TDI combinations. The applications of the algebraic approach based on computational algebraic geometry, on the other hand, are mostly restricted to the first and the modified first-generation TDI. Besides, geometric TDI furnishes an intuitive physical interpretation about the synthesis of the virtual optical paths. In this paper, the geometric TDI is utilized to investigate the modified second-generation TDI combinations in conjunction with a ternary search algorithm. The distinction between the second-generation and modified second-generation TDI solutions is elaborated regarding the rate of change of the arm lengths with respect to the opposite cyclic directions. For the sixteen-link combinations, forty second-generation TDI solutions are recovered, among which nine of them are identified as the modified second-generation ones.

Pulsar timing array (PTA) is expected to detect gravitational wave background (GWB) in the nanohertz band within the next decade. This provides an opportunity to test the gravity theory and cosmology. A typical data analysis method to detect GWB is cross-correlation analysis. The overlap reduction function (ORF) plays an important role in the correlation data analysis of GWB. The present approach to dealing with the intricate integration in ORF is to use short-wave approximation to drop out the tricky terms. In this paper, we provide the full analytic expression of the ORF for PTA without any approximation for all possible polarizations allowed by modifications of general relativity. Compared with the numerical simulation and short-wave approximation, our results are more efficient and widely applicable. Especially for the scalar-longitudinal mode where the short-wave approximation is not available, our analytical expression is particularly significant.

Recent studies based on the notion of black hole pseudospectrum indicated substantial instability of the fundamental and high-overtone quasinormal modes. Besides its theoretical novelty, the details about the migration of the quasinormal mode spectrum due to specific perturbations may furnish valuable information on the properties of associated gravitational waves in a more realistic context. This work generalizes the matrix method for black hole quasinormal modes to cope with a specific class of perturbations to the metric featured by discontinuity, which is known to be intimately connected with the quasinormal mode structural instability. In practice, the presence of discontinuity poses a difficulty so that many well-known approaches for quasinormal modes cannot be straightforwardly applied. By comparing with other methods, we show that the modified matrix method is efficient, which can be used to solve for the low-lying modes with reasonable precision. Therefore, it might serve as an alternative gadget for relevant studies., 16 pages, 3 figures, and 4 tables

The residual gas damping in the enclosure surrounding a free-fall test mass is an important limiting factor for the sensitivity of some space detection missions. We present a constrained volume damping model for space-borne gravitational wave detection, which depends on the escape time needed for a molecule to diffuse out of the gap between two adjacent surfaces. Using a completely inelastic molecular collision prediction, we calculate the escape times in the two most common constrained volumes, cylinder and cuboid, respectively. Both calculations agree well with Monte Carlo simulations. Additionally, the theoretical model of the residual gas damping presented in this work is in good agreement with the experimental results in the ground torsion pendulum test of LISA and its precursor LISA Pathfinder.

A crucial challenge to the ongoing endeavor of spaceborne gravitational wave (GW) detection resides in the laser phase noise, typically 7 to 8 orders of magnitude above the inevitable noise. The arm locking technique was proposed to suppress the noise in pre-stabilized laser beams. Based on the feedback control theory, it is implemented by appropriate design of the signal routing architecture, particularly the controllers' transfer functions. Theoretically and experimentally, the technique has been demonstrated to be capable of suppressing the laser phase noise by approximately 2-4 orders of magnitude while taking into account various aspects such as the gain and distribution of nulls in the Bode plot and the laser frequency pulling associated with the Doppler frequency subtraction. Consequently, the resultant noise floor is composed of the sources attributed to the clock jitter, optical bench motion, test mass fluctuations, shot-noise phase fluctuations at the photodetectors, whereas the magnitudes of these noises largely remain unchanged during the process. Besides, the original GW signals are deformed through the arm-locking control loop and therefore bear specific features governed by the associated arm-locking scheme. Nonetheless, the remaining laser phase noise from the arm-locking feedback routing settles within the capability threshold of the time-delay interferometry (TDI). In this regard, it is generally understood that the output of arm locking furnishes the input of TDI, through which the residual noise is further reduced to the desired level at a post-processing stage. In this work, we investigate the specific schemes regarding how the arm locking output is processed further by the TDI algorithm. Specific forms of the TDI combinations are derived in accordance with suppressed laser phase noise and deformed signals of GW.

We generalize the combinatorial algebraic approach first proposed by Dhurandhar et al. to construct various classes of modified second-generation time-delay interferometry (TDI) solutions. The main idea behind the algorithm is to enumerate, in a given order, a specific type of commutator between two monomials defined by the products of particular time-displacement operators. On the one hand, the above commutators can be systematically rewritten as the elements of a left ideal, defined by the l.h.s. of the relevant equation for the TDI solution. On the other hand, these commutators are shown to vanish if we only keep up the first-order contributions regarding the rate of change of armlengths. In other words, each commutator furnishes a valid TDI solution pertaining to the given type of modified second-generation combinations. In this work, the original algorithm, which only involves time-delay operators, is extended by introducing the time-advance ones and then utilized to seek solutions of the Beacon, Relay, Monitor, Sagnac, and fully symmetric Sagnac types. We discuss the relation between the present scheme's solutions and those obtained by the geometric TDI approach, a well-known method of exhaustion of virtual optical paths. In particular, we report the results on novel Sagnac-inspired solutions that cannot be straightforwardly obtained using the geometric TDI algorithm. The average response functions, floor noise power spectral densities, and sensitivity functions are evaluated for the obtained solutions.

The Einstein Equivalence Principle (EEP) carries a pivotal role in understanding theory of gravity and spacetime. It guarantees the gravity to be understood as geometric phenomenon. Considering gravitational coupling of matter in the standard model extension, we propose a novel scheme using frequency measurements to limit the equivalence principle violations in normal matter. The proposal consists of the comparison of high-precision clocks, comoving with the freely falling frame. The experimental comparison of identical kind of clocks on Earth surface can be used to carry out the proposed test, which allows performing simultaneous tests of weak equivalence principle and gravitational redshift. From the existing experiments of Sr optical clocks, we present a simultaneous determination of Earth-dependent parameter $\beta_{\text{E}}$ and clock-dependent parameter $\xi_{\text{Sr}}$ at the level of $10^{-5}$, and in combination with the gravitational redshift experiments and lunar laser ranging, we also obtain a limit on standard model extension coefficients for Lorentz violation. This work provides another important fundamental physics application for the continuous-improvement accuracy of atomic or optical clocks., Comment: 11 pages, 5 figure, 3 tables

In this paper, we study the quasinormal mode and late-time tail of charged massless scalar perturbations of a black hole in the generalized Rastall gravity. The black hole metric in question is spherically symmetric, accompanied by a power-Maxwell field surrounded by a quintessence fluid. It is shown that the massless scalar field, when {\it dressed up} with the magnetic field, acquires an effective mass which, in turn, significantly affects the properties of the resultant quasinormal oscillations and late-time tails. To be specific, the quasinormal frequencies become distorted and might even be unstable for particular spacetime configurations. Also, the exponent of the usual power-law tail is modified in accordance with the modification in the structure of the branch cut of the retarded Green's function. In particular, as the effective mass is generated dynamically due to the presence of the magnetic field, one may consider a process through which the field is gradually removed from the spacetime configuration. In this context, while the quasinormal oscillations converge to the case of massless perturbations, we argue that the properties of resultant late-time tails do not fall back to their massless counterpart. The relevant features are investigated by numerical and analytic approaches., Accepted for publication on CPC, doi: 10.1088/1674-1137/ac7855

Atom interferometry provides an important method of high-precision absolute gravity measurement. As absolute gravimeters, various systematic errors of atom gravimeters have been identified and evaluated. Here a comprehensive evaluation of systematic errors for a transportable atom gravimeter Huazhong University of Science and Technology-Quantum Gravimeter (HUST-QG) is presented. HUST-QG exhibited a short-term sensitivity of 24 μGal Hz−1/2 and a combined uncertainty of 3 μGal. The operation and evaluation of HUST-QG for transportable gravity measurements during the 10th International Comparison of Absolute Gravimeters are discussed. And the degree of equivalence for HUST-QG in this comparison is 1.3 μGal, which supports our evaluation.

Direct observation of gravitational waves offers us numerous novel possibilities to further explore the Universe. In practice, the efficiency of the experimental facility for a given gravitational wave source can be measured in terms of the sensitivity function of the instrument. The latter essentially indicates the least incident amplitude required in order to achieve the desired level of the signal-to-noise ratio. Among others, the resultant sensitivity function depends on the specific polarization state of the incident gravitational wave as well as the spatial layout of the detector and its orientation to the wave source. Theoretically, Einstein's general relativity predicts two tensor polarization modes, from a total of six possible modes arising from an arbitrary perturbation of the spacetime metric. Therefore, in this context, the feasibility of measuring nontensorial polarization states provides access to an alternative theory of gravity. In the present study, we analytically evaluate the response functions for arbitrary time-delay interferometry combinations while enumerating all possible polarization modes. The derivation is accomplished by separating the average on the all-sky solid angle from the remaining expression, which, in turn, gives rise to a few factors independent of the time-delay interferometry combination in question. Moreover, we applied the obtained results to the LISA and TianQin missions, and the asymptotic behavior of the resultant sensitivity functions is analyzed and discussed. Among others, it is observed that, for Sagnac combinations, the averaged response function of the breathing mode attains zero at specific discrete frequencies. Such a frequency value corresponds to a multiple of the reciprocal of the one-way light propagation time along the detector arm, irrelevant to the orientation of the wave source. For all six polarization modes, the present findings can be readily applied to an arbitrary time-delay interferometry combination with improved efficiency and accuracy.

The chameleon model was proposed as a promising candidate for the dark energy screening mechanism. It is not straightforward to detect the fifth force mediated by the chameleon scalar field in a high-density environment, such as those in a ground-based laboratory. Nevertheless, short-range gravitational experiments such as the torsion pendulum experiment can provide strong constraints on the chameleon model. In this work, we constrain the chameleon model from a precise test of the inverse-square law at Huazhong University of Science and Technology. In particular, we take full advantage of the regular flat-plate structure of the test and attraction mass, which gives rise to accurate modeling for the chameleon force and torque. The derived analytical results on the chameleon torque are shown to agree well with those by numerical calculations. Subsequently, based on the experimental data, the parameter space of the chameleon model is analyzed, and the results are presented in terms of a more stringent constraint on the model parameters.

The principal aim of the space-based gravitational wave detectors is to explore the gravitational waves in the 0.1 mHz-1 Hz frequency band. To maximize the potential capability of the experimental apparatus regarding the instrument performance, one needs to acquire accurate information on its sensitivity limit. The sensitivity curve in question, by definition, depends on the amplitudes of signal and noise involved in the measurement. In this work, we explicitly derive, under rather universal assumptions irrelevant to the detailed form of the time-delay interferometry combination, general results of the sensitivity functions. The key feature of the present approach is that both the all-sky and polarization average can be factorized and henceforth evaluated analytically. The resultant expressions are then applied to a variety of time-delay interferometry combinations, inclusively for the optimal channels. In particular, the asymptotical forms of the sensitivity functions are obtained at the high and low frequency limits, and the subsequential implications are analyzed. When compared with the approaches in terms of numerical integration, the obtained formulism furnishes a more straightforward as well as efficient access to the relevant signal noise ratios for the spaceborne gravitational wave detectors.

The TianQin Project is aiming at gravitational wave (GW) detection in space. TianQin GW observatory comprises three satellites orbiting on 1 × 105 km Earth orbits to form an equilateral-triangle constellation. In order to minimize the variations in arm lengths and breathing angles, the satellites must be launched and adjusted precisely into an optimized orbit. Therefore, satellite laser ranging must be used to enhance the precision of satellite orbit determination. To develop the capability of satellite laser ranging for TianQin’s orbit, the TianQin Laser Ranging Station has been designed and constructed to perform high-precision laser ranging for TianQin satellites and lunar laser ranging as well. Applying a 1064 nm Nd: YAG laser with 100 Hz repetition frequency, 80 pico-second pulse duration, and 2 × 2 array of superconducting nanowire single-photon detectors, we have obtained the laser echo signals from the five lunar retro-reflector arrays, and the measurement data have been packaged into 234 normal points (NPs), including a few data measured during the full-moon lunar phase. Each NP is calculated from continuous measurement for about ten minutes and the statistical error of the NPs is about 7 mm (1σ).

Short-range tests of the gravitational inverse-square law are very important for finding new interactions. In order to further improve the constraints on the Yukawa-like gravitational force, we propose a new scheme based on the torsion balance, where the speculative Yukawa-like gravitational force between the pendulum and the attractor is substantially increased by increasing the area of the test mass and the source mass. A dual-compensation design is used to realize a null experiment, which can release the accuracy requirement on some geometric parameters. The calculation result shows that, at the 95% confidence level, the new design can establish the strongest bound on the magnitude α of the Yukawa violation at the range of 40–800 μm with the total error of about 2.0 × 10−17 N m, and improve the previous bounds about one order of magnitude at the length scale λ ≈ 300 μm.

For the experiments of testing the Newtonian inverse-square law (ISL) at short range, we have analyzed the residual gas damping effect under the assumption of the temperature of the gas is isothermal (Ke J et al 2020 Class. Quantum. Grav. 37 205008). However, when the test mass squeezes the gas, the temperature of the gas will change accordingly and may cause additional noise. It is essential to study this phenomenon in pursuit of higher precision test of ISL. Here, we discuss the non-isothermal squeeze film damping by using the differential equations of energy conservation and change in molecular density. The results show that this kind of Brownian motion torque noise is larger than that estimated previously and is influenced by the degrees of freedom of molecules. Namely, a larger accessible distance between test bodies is needed in comparison to the internal damping of the pendulum.

Experiments measuring the Newtonian gravitational constant $G$ can offer uniquely sensitive probes of the test of the gravitational inverse-square law. An analysis of the non-Newtonian effect in two independent experiments measuring $G$ is presented, which permits a test of the $1/{r}^{2}$ law at the centimeter range. This work establishes the strongest bound on the magnitude $\ensuremath{\alpha}$ of Yukawa-type deviations from Newtonian gravity in the range of 5--500 mm and improves the previous bounds by up to a factor of 7 at the length range of 60--100 mm.

The ongoing development of the space-based laser interferometer missions is aiming at unprecedented gravitational wave detections in the millihertz frequency band. The spaceborne nature of the experimental setups leads to a degree of subtlety regarding the otherwise overwhelming laser frequency noise. The cancellation of the latter is accomplished through the time-delay interferometry technique. Moreover, to eventually achieve the desired noise level, the phase fluctuations of the onboard ultra-stable oscillator must also be suppressed. This can be fulfilled by introducing sideband signals which, in turn, give rise to an improved cancellation scheme accounting for the clock-jitter noise. Nonetheless, for certain Sagnac-type interferometry layouts, it can be shown that resultant residual clock noise found in the literature can be further improved. In this regard, we propose refined cancellation combinations for two specific clock noise patterns. This is achieved by employing the so-called geometric time-delay interferometry interpretation. It is shown that for specific Sagnac combinations, the residual noise diminishes significantly to attain the experimentally acceptable sensitivity level. Moreover, we argue that the derived combination, in addition to the existing ones in the literature, furnishes a general-purpose cancellation scheme that serves for arbitrary time-delay interferometry combinations. The subsequential residual noise will only involve factors proportional to the commutators between the delay operators. Our arguments reside in the form of the clock noise expressed in terms of the coefficients of the generating set of the first module of syzygies, the linear combination of which originally constitutes the very solution for laser noise reduction.

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., 16 pages, 1 figure, invited article to a special section in PTEP

Given the high-precision modern space mission, a precise relativistic modeling of observations is required. By solving the eikonal equation with the post-Newtonian approximation, the light propagation is determined by the iterative method in the gravitational field of an isolated, gravitationally bound N-body system. Different from the traditional $N$ bodies that are independent with each other in the system, our system includes the velocities, accelerations, gravitational interactions and tidal deformations of the gravitational bodies. The light delays of these factors then are precisely determined by the analytical solutions. These delays are significant and are likely to reach a detectable level for the \emph{strong} gravitational fields, such as binary pulsars and some gravitational wave sources. The result's application in the vicinity of the Earth provides a relativistic framework for modern space missions. From the relativistic analysis in the TianQin mission, we find the possible tests for the alternative gravitational theories, such as a possible determination for the post-Newtonian parameter $\gamma$ in the level of some scalar-tensor theories of gravity.

In the recent CODATA-2014 adjustment, the $G$ values obtained by different groups are not in good agreement with each other within respective uncertainties, which may be attributed to the possible unknown or incorrectly evaluated systematic errors in different methods. This paper proposes a scheme to measure $G$ with two independent methods. The first method is the extraction of the $G$ value from the fundamental periods of the torsion pendulum, with the source masses at two positions; the other one determines the $G$ value on the basis of the amplitude of the third-order harmonic component of the torsion pendulum. Both methods are performed with the same setup by using the large-amplitude torsion pendulum. Through theoretical derivation and simulation, the uncertainties of the $G$ values obtained by the two methods are both expected to be within 20 ppm. By comparing the $G$ values from the two methods, we can explore the potential systematic errors in the measurement.

The Newtonian gravitational constant, G, is one of the most fundamental constants of nature, but we still do not have an accurate value for it. Despite two centuries of experimental effort, the value of G remains the least precisely known of the fundamental constants. A discrepancy of up to 0.05 per cent in recent determinations of G suggests that there may be undiscovered systematic errors in the various existing methods. One way to resolve this issue is to measure G using a number of methods that are unlikely to involve the same systematic effects. Here we report two independent determinations of G using torsion pendulum experiments with the time-of-swing method and the angular-acceleration-feedback method. We obtain G values of 6.674184 × 10−11 and 6.674484 × 10−11 cubic metres per kilogram per second squared, with relative standard uncertainties of 11.64 and 11.61 parts per million, respectively. These values have the smallest uncertainties reported until now, and both agree with the latest recommended value within two standard deviations.

The Newtonian gravitational constant G has proved to be one of the most difficult constants to measure in physics. The improvement of measuring G with the atomic interferometry method is significantly limited by the positioning accuracy of the atom clouds and source masses, and the measurement accuracy of the atomic velocity. In this article, we propose an idea for designing the source masses to determine G with atom interferometry, in which a nearly uniform gravitational field in the motion region of the atom clouds is constructed. This design can greatly reduce the influence of the uncertainty of the atomic initial position and velocity on the precision of G measurement, since these atomic initial conditions affect the interferometer phase shift by coupling themselves with the gravitational gradient. Finally, we present a scheme for measuring G with a relative standard uncertainty of 27 parts per million.

Traditional torque type gravity gradiometer has an important pole in gravity gradient measurements, while it is relatively inefficient and with the precision of about 1 E mainly caused by the static operating mode. In this paper, we develop an improved torque type gravity gradiometer to improve the measuring efficiency, which is based on the dynamic modulation. The dynamic modulation keeps the gradiometer rotating on a turntable steadily, measures the deflection angle of the torsion pendulum continuously and then obtains the gravity gradients. The result shows that after using the improved gradiometer, the gradients W xz and W yz are obtained with precisions of 0.45 E and 0.32 E respectively in a cycle of 20 min.

We improve the test of the gravitational inverse-square law at the submillimeter range by suppressing the vibration of the electrostatic shielding membrane to reduce the disturbance coupled from the residual surface potential. The result shows that, at a 95% confidence level, the gravitational inverse-square law holds ($|\ensuremath{\alpha}|\ensuremath{\le}1$) down to a length scale $\ensuremath{\lambda}=48\text{ }\text{ }\ensuremath{\mu}\mathrm{m}$. This work establishes the strongest bound on the magnitude $\ensuremath{\alpha}$ of the Yukawa violation in the range of $40--350\text{ }\text{ }\ensuremath{\mu}\mathrm{m}$, and improves the previous bounds by up to a factor of 3 at the length scale $\ensuremath{\lambda}\ensuremath{\approx}70\text{ }\text{ }\ensuremath{\mu}\mathrm{m}$. Furthermore, the constraints on the power-law potentials are improved by about a factor of 2 for $k=4$ and 5.

In this paper, we study the quasinormal modes of the massless Dirac field for charged black holes in Rastall gravity. The spherically symmetric black hole solutions in question are characterized by the presence of a power-Maxwell field, surrounded by the quintessence fluid. The calculations are carried out by employing the WKB approximations up to the thirteenth order, as well as the matrix method. The temporal evolution of the quasinormal modes is investigated by using the finite difference method. Through numerical simulations, the properties of the quasinormal frequencies are analyzed, including those for the extremal black holes. Among others, we explore the case of a second type of extremal black holes regarding the Nariai solution, where the cosmical and event horizon coincide. The results obtained by the WKB approaches are found to be mostly consistent with those by the matrix method. It is demonstrated that the black hole solutions for Rastall gravity in asymptotically flat spacetimes are equivalent to those in Einstein gravity, featured by different asymptotical spacetime properties. As one of its possible consequences, we also investigate the behavior of the late-time tails of quasinormal models in the present model. It is found that the asymptotical behavior of the late-time tails of quasinormal modes in Rastall theory is governed by the asymptotical properties of the spacetimes of their counterparts in Einstein gravity., Comment: 19 pages, 6 figures, and 2 tables

Made available in DSpace on 2020-12-10T17:30:50Z (GMT). No. of bitstreams: 0 Previous issue date: 2019-12-01 National Natural Science Foundation of China (NNSFC) Post-doctoral Science Foundation of China Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) In this paper, the scalar quasinormal modes of nonlinear charged black hole metrics in Rastall gravity is investigated. The electromagnetic tensor presented in the background spacetime possesses a power-law form, and the system is assumed to be surrounded by a quintessence field. By utilizing the recently obtained analytic form of the metric, the quasinormal frequencies are obtained via the matrix method. The numerical values have been further compared against those evaluated by using the WKB approximation up to thirteenth order. Also, the finite difference method is utilized to study the temporal evolution of the scalar perturbations. In terms of calculations carried out for both massless and massive scalar fields, we discuss the properties of the resultant quasinormal frequencies, as well as their dependences on the model parameters describing the background black hole. To be specific, the effect of the electric charge, mass of the scalar field, and equation of state of the quintessence are examined. Besides, the quasinormal frequencies associated with an extremal black hole regarding the Nariai limit is explored, where the obtained results are found to be consistent with theoretical arguments. The black hole metric is found to be stable against scalar perturbations, in the presence of both linear and nonlinear electromagnetic fields. Copyright (C) EPLA, 2020 Huazhong Univ Sci & Technol, MOE Key Lab Fundamental Phys Quant Measurement, Hubei Key Lab Gravitat & Quantum Phys, PGMF, Wuhan 430074, Hubei, Peoples R China Huazhong Univ Sci & Technol, Sch Phys, Wuhan 430074, Hubei, Peoples R China China Univ Geosci, Hubei Subsurface Multiscale Imaging Key Lab, Inst Geophys & Geomat, Wuhan 430074, Hubei, Peoples R China Univ Sao Paulo, Escola Engn Lorena, BR-12602810 Lorena, SP, Brazil Univ Estadual Paulista, Fac Engn Guaratingueta, BR-12516410 Guaratingueta, SP, Brazil Yangzhou Univ, Ctr Gravitat & Cosmol, Sch Phys Sci & Technol, Yangzhou 225002, Jiangsu, Peoples R China Univ Estadual Paulista, Fac Engn Guaratingueta, BR-12516410 Guaratingueta, SP, Brazil National Natural Science Foundation of China (NNSFC): 11805166 National Natural Science Foundation of China (NNSFC): 11805074 National Natural Science Foundation of China (NNSFC): 91636221 Post-doctoral Science Foundation of China: 2017M620308 Post-doctoral Science Foundation of China: 2018T110750

The Newtonian gravitational constant G, which is one of the most important fundamental physical constants in nature, plays a significant role in the fields of theoretical physics, geophysics, astrophysics and astronomy. Although G was the first physical constant to be introduced in the history of science, it is considered to be one of the most difficult to measure accurately so far. Over the past two decades, eleven precision measurements of the gravitational constant have been performed, and the latest recommended value for G published by the Committee on Data for Science and Technology (CODATA) is (6.674 08 ± 0.000 31) × 10−11 m3 kg−1 s−2 with a relative uncertainty of 47 parts per million. This uncertainty is the smallest compared with previous CODATA recommended values of G; however, it remains a relatively large uncertainty among other fundamental physical constants. In this paper we briefly review the history of the G measurement, and introduce eleven values of G adopted in CODATA 2014 after 2000 and our latest two values published in 2018 using two independent methods.

Time-delay interferometry is put forward to improve the signal-to-noise ratio of space-borne gravitational wave detectors by canceling the large laser phase noise with different combinations of measured data. Based on the Michelson data combination, the sensitivity function of the detector can be obtained by averaging the all-sky wave source positions. At present, there are two main methods to encode gravitational wave signal into detector. One is to adapt gravitational wave polarization angle depending on the arm orientation in the gravitational wave frame, and the other is to divide the gravitational wave signal into plus and cross polarizations in the detector frame. Although there are some attempts using the first method to provide the analytical expression of sensitivity function, only a semianalytical one could be obtained. Here, starting with the second method, we demonstrate the equivalence of both methods. First time to obtain the full analytical expression of sensitivity function, which provides a fast and accurate mean to evaluate and compare the performance of different space-borne detectors, such as LISA and TianQin.

This work establishes a high-precision relativistic theoretical model: start from studying finite speed of light effect based on a coordinate transformation, and further extend the research methods to analyze the overall relativistic effects. This model promotes the development of testing General Relativity with atomic interferometry., Presented at the Eighth Meeting on CPT and Lorentz Symmetry, Bloomington, Indiana, May 12-16, 2019

The theory of general relativity has an ultraviolet(UV) problem that can be ameliorated by gravity with higher derivatives. The four-derivative gravity as an effective gravitational theory at UV scalars has two Yukawa-like corrections with parameters ${\ensuremath{\lambda}}_{0}$ and ${\ensuremath{\lambda}}_{2}$. By the analysis of experiments of HUST-2015, Newman's group, lake experiment, and Cassini spacecraft, we obtain the strong-bound regions for these parameters at submillimeter-to-millimeter, centimeter-to-meter, tens-of-meter, and solar-system scales, in which the properties of potential are clearly shown. Recently, the ghostfree and singularityfree gravity, a more potential modified gravity theory, introduces the novel conception of nonlocality. We test the scale of gravitational nonlocality ${\ensuremath{\lambda}}_{\mathrm{m}}l2.7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}\text{ }\text{ }\mathrm{m}$ by the torsion pendulum experiment HUST-2015. The predicted decaying spatial oscillations are visible meaning possible violation at shorter ranges. Our result provides useful information for gravitational interaction at microscopic ranges.