Gravitational Field Research Articles

Gravitational wave spectrum of chain inflation

Chain inflation is an alternative to slow-roll inflation in which the inflaton tunnels along a large number of consecutive minima in its potential. In this work we perform the first comprehensive calculation of the gravitational wave (GW) spectrum of chain inflation. In contrast to slow-roll inflation the latter does not stem from quantum fluctuations of the gravitational field during inflation, but rather from the bubble collisions during the first-order phase transitions associated with vacuum tunneling. Our calculation is performed within an effective theory of chain inflation which builds on an expansion of the tunneling rate capturing most of the available model space. The effective theory can be seen as chain inflation’s analog of the slow-roll expansion in rolling models of inflation. The near scale-invariance of the scalar power spectrum translates to a quasiperiodic shape of the inflaton potential in chain inflation, with the tunneling rate changing very slowly during the e-folds leading to cosmic microwave background observables. We show that chain inflation produces a very characteristic double-peak GW spectrum: a faint high-frequency peak associated with the gravitational radiation emitted during inflation, and a strong low-frequency peak associated with the graceful exit from chain inflation (marking the transition to the radiation-dominated epoch). There exist very exciting prospects to test the gravitational wave signal from chain inflation at the aLIGO-aVIRGO-KAGRA network, at LISA and /or at pulsar timing array experiments. A particularly intriguing possibility we point out is that chain inflation could be the source of the stochastic gravitational wave background recently detected by NANOGrav, PPTA, EPTA, and CPTA. We also show that the gravitational wave signal of chain inflation is often accompanied by running/ higher running of the scalar spectral index to be tested at future cosmic microwave background experiments. Published by the American Physical Society 2024

Realizing the Calculation of a Fully Normalized Associated Legendre Function Based on an FPGA

A large number of fully normalized associated Legendre function (fnALF) calculations are required to compute Earth’s gravity field elements using ultra high-order gravity field coefficient models. In the surveying and mapping industry, researchers typically rely on CPU-based systems for these calculations, which leads to limitations in execution speed and power efficiency. Although modern CPUs improve instruction execution efficiency through instruction-level parallelism, the constraints of a shared memory architecture impose further limitations on the execution speed and power efficiency. This results in exponential increases in computation time as demand rises alongside high power consumption. In this article, we present a new computational implementation of an fnALF based on the ZYNQ platform. We design a task-parallel “pipeline” architecture which converts the original serial logic into a more efficient hardware implementation, and we utilize a redundant calculation layer to handle repetitive coefficient computations separately. The experimental results demonstrate that our system achieved accurate and rapid calculations. Under the only one geocentric residual latitude condition, we measured the computation times for spherical harmonic coefficient degrees of 360, 720, and 1080 to be 0.155922 s, 0.520950 s, and 1.401609 s, respectively. In the case of the multiple geocentric residual latitudes condition, our design generally yielded efficiency gains of over three times those of MATLAB R2020b implementation. Additionally, our calculated results were used to determine the geoid height in the field with an error of less than ±0.1m, confirming the reliability of our computations.

On the role of fiducial structures in minisuperspace reduction and quantum fluctuations in LQC

Abstract In spatially non-compact homogeneous minisuperpace models, spatial integrals in the Hamiltonian and symplectic form must be regularised by confining them to a finite volume Vo , known as the fiducial cell. As this restriction is unnecessary in the complete field theory before homogeneous reduction, the physical significance of the fiducial cell has been largely debated, especially in the context of (loop) quantum cosmology. Understanding the role of Vo is in turn essential for assessing the minisuperspace description’s validity and its connection to the full theory. In this work we present a systematic procedure for the field theory reduction to spatially homogeneous and isotropic minisuperspaces within the canonical framework and apply it to both a massive scalar field theory and gravity. Our strategy consists in implementing spatial homogeneity via second-class constraints for the discrete field modes over a partitioning of the spatial slice into countably many disjoint cells. The reduced theory’s canonical structure is then given by the corresponding Dirac bracket. Importantly, the latter can only be defined on a finite number of cells homogeneously patched together. This identifies a finite region, the fiducial cell, whose physical size acquires then a precise meaning already at the classical level as the scale over which homogeneity is imposed. Additionally, the procedure allows us to track the information lost during homogeneous reduction and how the error depends on Vo . We then move to the quantisation of the classically reduced theories, focusing in particular on the relation between the theories for different Vo , and study the implications for statistical moments, quantum fluctuations, and semiclassical states. In the case of a quantum scalar field, a subsector of the full quantum field theory where the results from the ‘first reduced, then quantised’ approach can be reproduced is identified and the conditions for this to be a good approximation are also determined.

Optimization of global gravitational potential models with detailed gravity anomalies in Southern VietnamOptimization of global gravitational potential models with detailed gravity anomalies in Southern Vietnam

This study evaluates the accuracy of several global gravity field models, specifically EGM 2008, EICGEN-6C4, SGG-UGM-1, SGG-UGM-2, and GECO, using detailed gravity anomaly data from 1968 points in the southern plains of Vietnam. The evaluation process followed a rigorous methodology to ensure precision. Results indicate that these models exhibit similar accuracy levels in the experimental area, with a mean error of approximately 6.2 mGal. Among them, The SGG-UGM-2 model, demonstrated the highest precision, with a fluctuation range of -29.2425 to +74.9010 mGal. These newer generation models, which incorporate additional satellite data, offer enhanced reliability compared to the EGM2008 model. The fluctuation ranges for other models also varied: EGM 2008 from -29.8662 to +82.2140 mGal, EIGEN-6C4 from -28.3626 to +74.2292 mGal, SGG-UGM-1 from -28.9500 to +75.5315 mGal, and GECO from -30.5641 to +73.6775 mGal. This research highlights the critical importance of accurate gravity field models for various applications, including geodesy, geophysics, natural disaster management, resource exploration, and military operations. The methodologies employed for accuracy assessment are adaptable to other regions with similar datasets, underscoring the significance of precise geophysical measurements in Vietnam's diverse geographic landscape. The findings support the essential role of gravity anomaly data in understanding Earth's physical properties and emphasize the need for continued evaluation across different regions in Vietnam to establish comprehensive applicability. This research paves the way for advanced studies and practical applications, contributing to a deeper understanding of Earth's physical properties.

Eccentric mergers in AGN Discs: Influence of the supermassive black-hole on three-body interactions

Abstract There are indications that stellar-origin black holes (BHs) are efficiently paired up in binary black holes (BBHs) in Active Galactic Nuclei (AGN) disc environments, which can undergo interactions with single BHs in the disc. Such binary-single interactions can potentially lead to an exceptionally high fraction of gravitational-wave mergers with measurable eccentricity in LIGO/Virgo/KAGRA. We here take the next important step in this line of studies by performing post-Newtonian N-body simulations between migrating BBHs and single BHs set in an AGN disc-like configuration, with a consistent inclusion of the central supermassive black hole (SMBH) in the equations of motion. With this setup, we study how the fraction of eccentric mergers varies in terms of the initial size of the BBH semi-major axis relative to the Hill sphere, as well as how it depends on the angle between the BBH and the incoming single BH. We find that the fraction of eccentric mergers is still relatively large, even when the interactions are notably influenced by the gravitational field of the nearby SMBH. However, the fraction as a function of the BBH semi-major axis does not follow a smooth functional shape, but instead shows strongly varying features that originate from the underlying phase-space structure. The phase-space further reveals that many of the eccentric mergers are formed through prompt scatterings. Finally, we present the first analytical solution to how the presence of an SMBH in terms of its Hill sphere affects the probability for forming eccentric BBH mergers through chaotic three-body interactions.

Diffusion-driven flows in a nonlinear stratified fluid layer

Diffusion-driven flow is a boundary layer flow arising from the interplay of gravity and diffusion in density-stratified fluids when a gravitational field is non-parallel to an impermeable solid boundary. This study investigates diffusion-driven flow within a nonlinearly density-stratified fluid confined between two tilted parallel walls. We introduce an asymptotic expansion inspired by the centre manifold theory, where quantities are expanded in terms of derivatives of the cross-sectional averaged stratified scalar (such as salinity or temperature). This technique provides accurate approximations for velocity, density and pressure fields. Furthermore, we derive an evolution equation describing the cross-sectional averaged stratified scalar. This equation takes the form of the traditional diffusion equation but replaces the constant diffusion coefficient with a positive-definite function dependent on the solution's derivative. Numerical simulations validate the accuracy of our approximations. Our investigation of the effective equation reveals that the density profile depends on a non-dimensional parameter denoted as $\gamma$ representing the flow strength. In the large $\gamma$ limit, the system is approximated by a diffusion process with an augmented diffusion coefficient of $1+\cot ^{2}\theta$ , where $\theta$ signifies the inclination angle of the channel domain. This parameter regime is where diffusion-driven flow exhibits its strongest mixing ability. Conversely, in the small $\gamma$ regime, the density field behaves like pure diffusion with distorted isopycnals. Lastly, we show that the classical thin film equation aligns with the results obtained using the proposed expansion in the small $\gamma$ regime but fails to accurately describe the dynamics of the density field for large $\gamma$ .

Learning Gravity Fields of Small Bodies: Self-adaptive Physics-informed Neural Networks

The reconstruction of the gravity field within the surface region of small bodies is crucial for the surface proximity operations of a probe. However, the irregular shape, uneven mass distribution, and sparse gravitational data of small bodies pose challenges in the reconstruction. We propose a self-adaptive physics-informed neural network (PINN) for the reconstruction of the gravity field within the surface region of irregular and heterogeneous small bodies. First, we introduce an auxiliary-point-based data augmentation strategy to reduce the model’s dependency on the quantity of data. Second, we incorporate a residual-based adaptive sampling strategy to enhance the prediction accuracy of the model in regions with significant variations in small-body density. Finally, we introduce an adaptive weight module based on gradient ascent to mitigate the balancing issue of loss terms in the PINN. Experiments indicate that our algorithm achieves improved accuracy for reconstructing the gravity field within the surface region of small bodies. This work is expected to contribute to the enhancement of safety in surface proximity operations around the surfaces of small bodies.

Modified TRIAD Method for Solving the Problem of a Moving Object Orientation

Currently, it is relevant to create moving objects orientation systems based on the integration of various types of primary information sensors. One way to solve the orientation problem is to use the TRIAD (Tri-Axial Orientation Determination) method which allows determining the matrix of direction cosines between two coordinates. The traditional TRIAD force method is based on the use of two reference vectors – of gravitational and geomagnetic fields, measured by accelerometers and magnetometers, respectively. The disadvantage of this method is – appearance of additional deviations during the accelerated movement of the object and influence of primary information sensors’ random errors. Modified TRIAD method which is based on measurements of three triads of sensors: magnetometers, accelerometers and gyroscopes was proposed in the article. Estimates of acceleration vectors of gravitational and geomagnetic fields were calculated taking into account gyroscope measurements. Then these estimates were combined with the accelerometers’ and magnetometers’ data. The complex gravitational and geomagnetic fields’ accelerations were used to form the direction cosine matrix by the TRIAD method. The suggested modified method can be used to implement free-form moving objects’ orientation systems, since it is 6–8 times more accurate compared to the classic TRIAD method. Attenuation of random sensor errors and disturbances due to object acceleration can be adjusted by use of weigh factors.

Correlations and Signaling in the Schrödinger-Newton Model

Abstract The Schrödinger-Newton model is a semi-classical theory in which, in addition to mutual attraction, massive quantum particles interact with their own gravitational fields. While there are many studies on the phenomenology of single particles, correlation dynamics in multipartite systems is largely unexplored. Here, we show that the Schrödinger-Newton interactions preserve the product form of the initial state of a many-body system, yet on average agreeing with classical mechanics of continuous mass distributions. This leads to a simple test of the model, based on verifying bipartite gravitational evolution towards non-product states. We show using standard quantum mechanics that, with currently accessible single-particle parameters, two masses released from harmonic traps get correlated well before any observable entanglement is accumulated. Therefore, the Schrödinger-Newton model can be tested with setups aimed at observation of gravitational entanglement with significantly relaxed requirements on coherence time. We also present a mixed-state extension of the model that avoids superluminal signaling.

Optical aspects of Born-Infeld BTZ black holes in massive gravity

We explore the dynamics of thin accretion disks, the radius of black hole shadows, observed intensities, and the visual characteristics of Born-Infeld BTZ black holes in massive gravity. We find out the relations for angular velocity, specific energy, and angular momentum of particles around the black hole. We observe that intense Born-Infeld electromagnetic effects lead to a reduction in the rotational motion of particles within the accretion disk, and the massive gravity slows down the orbital motion of these particles. We reveal that the influence of massive gravity parameter correlates with a reduction in the black hole’s shadow size, which suggests that massive gravity effects intensify the gravitational fields, thereby reducing the angular diameter of the shadows. On the other hand, a higher Born-Infeld parameter enlarges the black hole’s shadow, which manifests a visual relationship between the black hole’s physical dimensions and its gravitational influence. Moreover, we also uncover the optical characteristics of Born-Infeld BTZ black holes, which show that the Born-Infeld parameter greatly influences the electromagnetic field around the black hole, which affects energy distribution in the space. Finally, we observe that massive gravity significantly influences the spacetime structure near black holes, which is crucial for grasping gravitational lensing and the dynamics of accretion disks under such extreme conditions.

Gravitational waves of nonextremal Kerr black holes from conformal symmetry

In the low-energy limit, the near region of a generic Kerr black hole has been conjectured to be holographically dual to a two-dimensional conformal field theory. In this paper, we consider a test object orbiting in the near region of a nonextremal Kerr black hole. We first couple it to a massless scalar field. The resulting scalar radiation at the horizon is computed from the perspectives of gravity and dual conformal field theory. Considering the influence of nonzero temperature, the agreement of both computations is found. Then, we generalize the analysis to the gravitational radiation and find agreement again. The agreement supports the conjectured holography and provides a potential theoretical tool for gravitational wave computations. Published by the American Physical Society 2024

System Tautochronic Path for Pendulum Vibration Absorber Based on Simple Harmonic Oscillator Transformation

Abstract Centrifugal pendulum vibration absorbers (CPVAs) are essentially collections of pendulums attached to a rotating component or components within a mechanical system for the purpose of mitigating the typical torsional surging that is inherent to internal combustion engines and electric motors. The dynamic stability and performance of CPVAs are highly dependent on the motion path defined for their pendulous masses. Assemblies of absorbers are tuned by adjusting these paths such that the pendulums respond to problematic orders (multiples of average rotation speed) in a way that smooths the rotational accelerations arising from combustion or other nonuniform rotational acceleration events. For most motion paths, pendulum tuning indeed shifts as a function of the pendulum response amplitude. For a given motion path, the tuning shift that occurs as pendulum amplitude varies produces potentially undesirable dynamic instabilities. Large amplitude pendulum motion that mitigates a high percentage of torsional oscillation while avoiding instabilities brought on by tuning shift introduces complexity and hazards into CPVA design processes. Therefore, identifying pendulum paths whose tuning order does not shift as the pendulum amplitude varies, so-called tautochronic paths, may greatly simplify engineering design processes for generating high-performing CPVAs. To illustrate this new approach and results, a tautochronic cutout shape producing constant period system motion is obtained for a simplified problem involving a mass sliding in the cutout of a larger mass that is free to translate horizontally without friction in a constant gravitational field, where the translating base mass replaces the rotating rotor in the centrifugal field.

Effect of Variable Gravity Field on Dual Component Convection in a Couple Stress Fluid Saturated Anisotropic Porous Layer With Temperature‐Dependent Heat Source

ABSTRACTThis study examines how gravity fluctuations, the couple stress parameter, anisotropic parameters, and heat source collectively influence dual‐component convection in the porous layer. The linear analysis is conducted utilizing the normal mode technique. The authors proposed three categories of gravity fluctuation, namely: (a) linear, (b) parabolic, and (c) exponential. Expressions for both stationary and oscillatory Rayleigh numbers are derived using the Galerkin approach. Neutral stability curves for both stationary and oscillatory modes are analyzed, with graphical representations to show the effects of various stability parameters, including gravity fluctuations, couple stress, anisotropy, and heat source. The results show that the mechanical anisotropy parameter and Vadasz number lead to system destabilization, while the couple stress parameter, Lewis number, gravity parameter, solute Rayleigh number, and thermal anisotropy parameter help to stabilize the system. Furthermore, the system is more stable with exponential gravity fluctuations and less stable with parabolic gravity fluctuations. This finding offers insights into thermal convective instability in porous media, impacting applications in geoscience, engineering, and environmental science.

Weighted Fusion Method of Marine Gravity Field Model Based on Water Depth Segmentation

Among the marine gravity field models derived from satellite altimetry, the Scripps Institution of Oceanography (SIO) series and Denmark Technical University (DTU) series models are the most representative and are often used to integrate global gravity field models, which were inverted by the deflection of vertical method and sea surface height method, respectively. The fusion method based on the offshore distance used in the EGM2008 model is just model stitching, which cannot realize the true fusion of the two types of marine gravity field models. In the paper, a new fusion method based on water depth segmentation is proposed, which established the Precision–Depth relationship of each model in each water depth segment in the investigated area, then constructed the FUSION model by weighted fusion based on the precision predicted from the Precision–Depth relationship at each grid in the whole region. The application in the South China Sea shows that the FUSION model built by the new fusion method has better accuracy than SIO28 and DTU17, especially in shallow water and offshore areas. Within 20 km offshore, the RMS of the FUSION model is 5.10 mGal, which is 8% and 4% better than original models, respectively. Within 100 m of shallow water, the accuracy of the FUSION model is 4.01 mGal, which is 14% and 12% higher than the original models, respectively. A further analysis shows that the fusion model is in better agreement with the seabed topography than original models. The new fusion method can blend the effective information of original models to provide a higher-precision marine gravity field.

Precise Geoid Determination in the Eastern Swiss Alps Using Geodetic Astronomy and GNSS/Leveling Methods.

Astrogeodetic deflections of the vertical (DoVs) are close indicators of the slope of the geoid. Thus, DoVs observed along horizontal profiles may be integrated to create geoid undulation profiles. In this study, we collected DoV data in the Eastern Swiss Alps using a Swiss Digital Zenith Camera, the COmpact DIgital Astrometric Camera (CODIAC), and two total station-based QDaedalus systems. In the mountainous terrain of the Eastern Swiss Alps, the geoid profile was established at 15 benchmarks over a two-week period in June 2021. The elevation along the profile ranges from 1185 to 1800 m, with benchmark spacing ranging from 0.55 km to 2.10 km. The DoV, gravity, GNSS, and levelling measurements were conducted on these 15 benchmarks. The collected gravity data were primarily used for corrections of the DoV-based geoid profiles, accounting for variations in station height and the geoid-quasigeoid separation. The GNSS/levelling and DoV data were both used to compute geoid heights. These geoid heights are compared with the Swiss Geoid Model 2004 (CHGeo2004) and two global gravity field models (EGM2008 and XGM2019e). Our study demonstrates that absolute geoid heights derived from GNSS/leveling data achieve centimeter-level accuracy, underscoring the precision of this method. Comparisons with CHGeo2004 predictions reveal a strong correlation, closely aligning with both GNSS/leveling and DoV-derived results. Additionally, the differential geoid height analysis highlights localized variations in the geoid surface, further validating the robustness of CHGeo2004 in capturing fine-scale geoid heights. These findings confirm the reliability of both absolute and differential geoid height calculations for precise geoid modeling in complex mountainous terrains.

Influence of GUP corrected Casimir energy on zero tidal force wormholes in modified teleparallel gravity with matter coupling

In recent times, the study of the Casimir effect in quantum field theory has garnered increasing attention because of its potential to be an ideal source of exotic matter needed for stabilizing traversable wormholes. It has been confirmed through experimental evidence that this phenomenon involves fluctuations in the vacuum field, leading to a negative energy density. Motivated by the above, we have investigated Casimir wormholes with corrections from the Generalized Uncertainty Principle (GUP) within the framework of matter-coupled teleparallel gravity. Our analysis includes three well-known GUP models: the Kempf, Mangano, and Mann (KMM) model, the Detournay, Gabriel, and Spindel (DGS) model, and a third model called Model II. For a broader analysis, we have considered two well-known model functions for the teleparallel theory: a linear f(T,T)=αT+βT\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f(T,\\mathcal {T})=\\alpha T+\\beta \\mathcal {T}$$\\end{document} and a quadratic model f(T,T)=ηT2+χT\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f(T,\\mathcal {T})=\\eta T^2+\\chi \\mathcal {T}$$\\end{document}. The shape function solutions corresponding to both models are examined in the absence of tidal forces in spacetime. We also demonstrate the crucial role played by the parameters of the f(T,T)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f(T,\\mathcal {T})$$\\end{document} models in the violation of the energy conditions. With the increasing interest in detecting gravitational waves from astrophysical objects, we have thoroughly discussed the perturbation of the wormhole solutions in the scalar, electromagnetic, axial gravitational, and Dirac field backgrounds. We employ the 3rd order WKB expansion to find the complex frequencies associated with the quasinormal modes of energy dissipation. Additionally, we also calculate the active mass and total gravitational energy for the wormhole geometry. The amount of exotic matter involved in sustaining these wormholes is also found in this paper. Furthermore, the physical stability of such Casimir wormholes is examined using the Tolman–Oppenheimer–Volkoff equation.

Nonlinear Perturbations and Weak Shock Waves in Isentropic Atmospheres

Acoustic perturbations to stellar envelopes can lead to the formation of weak shock waves via nonlinear wave steepening. Close to the stellar surface, the weak shock wave increases in strength and can potentially lead to the expulsion of part of the stellar envelope. While accurate analytic solutions to the fluid equations exist in the limits of low-amplitude waves or strong shocks, connecting these phases generally requires simulations. We address this problem using the fact that the plane-parallel Euler equations, in the presence of a constant gravitational field, admit exact Riemann invariants when the flow is isentropic. We obtain exact solutions for acoustic perturbations and show that after they steepen into shock waves, Whitham’s approximation can be used to solve for the shock’s dynamics in the weak to moderately strong regimes, using a simple ordinary differential equation. Numerical simulations show that our analytic shock approximation is accurate up to moderate (∼few–15) Mach numbers, where the accuracy increases with the adiabatic index.

Constraining anisotropic universe under f(R,T) theory of gravity

We try to find the possibility of a Bianchi V universe in the modified gravitational field theory of f(R,T). We have considered a Lagrangian model in connection between the trace of the energy-momentum tensor T and the Ricci scalar R. In order to solve the field equations a power law for the scaling factor was also considered. To make a comparison of the model parameters with the observational data we put constraint on the model under the datasets of the Hubble parameter, Baryon Acoustic Oscillations, Pantheon, joint datasets of Hubble parameter + Pantheon and collective datasets of the Hubble parameter + Baryon Acoustic Oscillations + Pantheon. The outcomes for the Hubble parameter in the present epoch are reasonably acceptable, especially our estimation of this H0 is remarkably consistent with various recent Planck Collaboration studies that utilize the Λ-CDM model.

McVittie–Plummer Spacetime: Plummer Sphere Immersed in the FLRW Universe

The McVittie–Plummer spacetime is a spherically symmetric inhomogeneous cosmological model that represents a spherical star system embedded in a standard Friedmann–Lemaître–Robertson–Walker (FLRW) cosmological model. We study the main physical properties of this gravitational field. Regarding the interplay between the physics of the local system and the expanding background, we employ the Misner–Sharp mass–energy function to show that there is a relatively weak time-dependent general relativistic coupling between the astrophysical system and the background FLRW cosmological model. The coupling term is proportional to the inverse of the scale factor and decreases as the Universe expands.

Estimating the possible QPOs of [formula omitted] from the parameters of a hairy Kerr black hole

In this paper, we study the dynamics of the shock cone formed around a hairy Kerr black hole due to Bondi-Hoyle-Lyttleton (BHL) accretion and investigate the quasi-periodic oscillations (QPO) behaviors resulting from the black hole-cone interaction, aiming to predict the QPO frequencies that may occur around the M87∗ black hole. To achieve this, we use the hairy Kerr black hole parameters consistent with the observed shadow parameters of M87∗ as initial conditions in numerical simulations, revealing the structure of the resulting shock cone and QPOs in a strong gravitational field. Numerical calculations show that the deviation of the hairy Kerr black hole from the Kerr metric and the hair parameters significantly influence the complex behavior of the resulting QPOs. It is found that the Lense-Thirring effect and the pressure modes trapped within the cone lead to the excitation of QPOs. The hair parameter has been observed to suppress the resulting QPO frequencies. The Lense-Thirring effect, in a strong gravitational field with a black hole spin parameter of a/M>0.7, also suppresses other modes and generates high-frequency QPOs. It is predicted that the QPO frequencies observed around the M87∗ black hole could span a wide range from nHz to mHz. Using both Kerr and hairy Kerr gravities, the QPO frequencies formed around the M87∗ black hole can be explained. Especially in cases where the black hole is spinning rapidly, power spectrum density (PSD) analyses have shown very distinct low-frequency QPOs and resonance conditions in both gravities. By comparing the results obtained from numerical calculations with observational and analytical results, we discuss the observability of the QPO frequencies that may occur around the M87∗ black hole.