Riccardo Della Monica, Ivan de Martino, Mariafelicia de Laurentis
The explicit derivation for the orbital precession of the S2 star in the Galactic Center in the Scalar-Tensor-Vector Gravity is discussed and compared with previous research. The two different predictions are validated by numerically integrating the geodesic equations for a test particle.
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This is a comment on the recent paper by G. S. Adkins and J. McDonnell ``Orbital precession due to central-force perturbations'' published in Phys. Rev. D75 (2007), 082001 [arXiv:gr-qc/0702015]. We show that the main result of this paper, the formula for the precession of Keplerian orbits induced by central-force perturbations, can be obtained very simply by the use of Hamilton's vector.
A novel approximation method in studying the perihelion precession and planetary orbits in general relativity is to use geodesic deviation equations of first and high-orders, proposed by Kerner et.al. Using higher-order geodesic deviation approach, we generalize the calculation of orbital precession and the elliptical trajectory of neutral test particles to Kerr$-$Newman space-times. One of the advantage of this method is that, for small eccentricities, one obtains trajectories of planets without using Newtonian and post-Newtonian approximations for arbitrary values of quantity ${G M}/{R c^2}$…
The GRAVITY Collaboration achieved the remarkable detection of the orbital precession of the S2 star around the Galactic centre supermassive black hole, providing yet another proof of the validity of the General Relativity. The departure from the Schwarzschild precession is encoded in the parameter $f_{\rm SP}$ which multiplies the predicted general relativistic precession. Such a parameter results to be $f_{\rm SP}=1.10\pm0.19$, which is consistent with General Relativity ($f_{\rm SP}=1$) at 1$σ$ level. Nevertheless, this parameter may also hide an effect of modified theories of gravity. Thus…
We calculate the precession of Keplerian orbits under the influence of arbitrary central-force perturbations. Our result is in the form of a one-dimensional integral that is straightforward to evaluate numerically. We demonstrate the effectiveness of our formula for the case of the Yukawa potential. We obtain analytic results for potentials of the form V(r) = αr^n and V(r) = α\ln(r/λ) in terms of the hypergeometric function {_2F_1} (1/2-n/2,1-n/2; 2; e^2), where e is the eccentricity. Our results reproduce the known general relativistic (n=-3), constant force (n=1), and cosmological constant (…
Binary black-hole systems are expected to be important sources of gravitational waves for upcoming gravitational-wave detectors. If the spins are not colinear with each other or with the orbital angular momentum, these systems exhibit complicated precession dynamics that are imprinted on the gravitational waveform. We develop a new procedure to match the precession dynamics computed by post-Newtonian (PN) theory to those of numerical binary black-hole simulations in full general relativity. For numerical relativity NR) simulations lasting approximately two precession cycles, we find that the P…
We have obtained the first constraint of the parameter space of Scalar-Tensor-Vector-Gravity using the motion of the S2-star around the supermassive black hole at the centre of the Milky Way, and we did not find any serious tension with General Relativity. We used the Schwarzschild-like metric of Scalar-Tensor-Vector-Gravity to predict the orbital motion of S2-star, and to compare it with the publicly available astrometric data, which include 145 measurements of the positions, 44 measurements of the radial velocities of S2-star along its orbit, and the recent measurement of the orbital precess…
Spin precession in general stationary and axisymmetric spacetimes
本文研究一般稳态轴对称时空中试验粒子的自旋进动，推导两种情形下的进动角并在克尔-纽曼时空中分析，应用于天文系统验证吻合且预测木星卫星的进动效应可探测。
Parity-violating corrections to the orbital precession of binary system
针对PSR J1141-6545双星系统，采用含场源内外项的宇称破缺引力度规计算轨道进动修正，明确其与GR的本质差异，给出了宇称破缺理论参数的观测约束。
We estimate the parameters of Hybrid Palatini gravity model with the Schwarzschild precession of S-stars, specifically of S2, S38 and S55 stars. We also take into account case of bulk mass distribution near Galactic Center. We assume that the Schwarzschild orbital precession of mentioned S-stars is the same like in General Relativity (GR) in all studied cases. In 2020 the GRAVITY Collaboration detected the orbital precession of the S2 star around the supermassive black hole (SMBH) at the Galactic Center and showed that it is close to the GR prediction. The astronomical data analysis of S38 and…
We discuss the influence of the cosmological constant on the gravitomagnetic clock effect and the gravitational time delay of electromagnetic rays. Moreover, we consider the relative motion of a binary system to linear order in the cosmological constant $Λ$. The general expression for the effect of $Λ$ on pericenter precession is given for arbitrary orbital eccentricity.
Nonlinear Orbital Variations in Binary Radio Pulsars from Lense-Thirring Precession
研究通过二元射电脉冲星非线性轨道变化探测Lense-Thirring进动，为约束脉冲星转动惯量提供新方法。
Spherical Orbital Dynamics and Relativistic Precession in Kerr-MOG Spacetime
本文基于 Hamilton-Jacobi 形式研究了 Kerr-MOG 黑洞周围球面轨道的动力学与相对论进动，发现 MOG 参数对交点和近星点进动及陀螺仪自旋进动有显著影响，为检验广义相对论偏差提供了观测探针。
Orbital dynamics and spin-precession around a circular chiral vorton
研究 chiral vorton 的轨道动力学和自旋进动，揭示其独特的进动特征，为观测 vorton 提供可能的途径。
C. M. Will in a recent Letter [arXiv:1802.05304] predicts a new Mercury's precession rate which is $100$ times larger than the second-post-Newtonian contribution, our calculation is about $30$ times larger. Thus the new Mercury's precession rate is about $6.4\ast 10^{-8}$, instead of $6.2\ast 10^{-8}$, degrees per century.
Orbital precession of stars in the Galactic center
基于S2星轨道进动的观测，通过后牛顿轨道积分方法，研究表明需考虑高阶PN项以精确确定角进动，从而同时测量银河系中心超大质量黑洞的质量与自转。
Orbital precession and other properties of two-body motion in the presence of dark energy
本文研究存在宇宙学常数Λ的开普勒两体问题，通过无量纲参数识别轨道类型，刻画运动定性特征并求解临界参数，为暗能量影响下的天体两体运动分析提供了理论依据。
Recent article "Revisiting the 2PN Pericenter Precession in View of Possible Future Measurements" published by Iorio (Universe, 2020) argues that calculations of the secular 2PN precession of the orbital pericenter of a binary system accomplished by Damour and Schaefer (Nuovo Cim. B, 1988) and by Kopeikin and Potapov (Astron. Rep., 1994) with different mathematical techniques are inconsistent, differ from each other and do not agree with the result obtained by Iorio (Universe, 2020). The purpose of this communication is to demonstrate that the article by Iorio is erroneous, suffers from miscon…
The LIGO--Virgo--KAGRA collaborations (LVK) produced a catalogue containing gravitational-wave (GW) observations from the first half of the third GW observing run (O3a). This catalogue, GWTC-2.1, includes for the first time a number of \emph{exceptional} GW candidates produced from merging black-hole-binaries with unequivocally unequal component masses. Since subdominant multipole moments and spin-induced orbital precession are more likely to leave measurable imprints on the emitted GW from unequal component mass binaries, these general relativistic phenomena may now be measurable. Indeed, bot…
General relativistic spin-orbit interaction leads to the quasiresonant oscillation of the gyroscope mass center along the orbital normal. The beating amplitude does not include the speed of light and equals the ratio of the intrinsic momentum of the gyroscope to its orbital momentum. The modulation frequency equals the angular velocity of the geodetic precession that prevents the oscillation from resonance. The oscillation represents the precession of the gyroscope orbital momentum. Within an acceptable time the oscillation amplitude reaches the values that are amenable to being analyzed exper…
We investigate the relativistic effects in the orbital motion of the exoplanet HD80606b with a high eccentricity of $e\simeq0.93$ .We propose a method to detect these effects (notably the orbital precession) based on measuring the successive eclipse and transit times of the exoplanet. In the case of HD80606b, we find that in ten years (after approximately 33 periods) the instants of transits and eclipses are delayed with respect to the Newtonian prediction by about three minutes due to relativistic effects. These effects can be detected by comparing at different epochs the time difference betw…
The inclusion of aligned-spin effects in gravitational-wave search pipelines for neutron-star--black-hole binary coalescence has been shown to increase the astrophysical reach with respect to search methods where spins are neglected completely, under astrophysically reasonable assumptions about black-hole spins. However, theoretical considerations and population synthesis models suggest that many of these binaries may have a significant misalignment between the black-hole spin and the orbital angular momentum, which could lead to precession of the orbital plane during the inspiral and a conseq…
Spin precession effects in the phasing formula of eccentric compact binary inspirals up to the second post-Newtonian order
本文研究偏心紧凑二体系统中轨道偏转与自旋偏转的耦合动力学，通过分离时间尺度并应用预偏平均方法，推导出闭合形式的相位公式，提升引力波信号建模的精度与计算效率。
Probing a Lorentz-violating parameter from orbital precession of the S2 star around the galactic centre supermassive black hole
本文利用S2星轨道数据，在bumblebee引力理论框架下，通过马尔可夫链蒙特卡洛分析，探测到洛伦兹破坏参数ℓ的约束，结果比事件视界望远镜观测更精确。
Comment on "Regular magnetically charged black holes from nonlinear electrodynamics: Thermodynamics, light deflection, and orbital dynamics" by Aydiner, Sucu and Sakalli
该评论指出因作者和隶属关系存疑，原论文已被arXiv撤回。
We present a simple method to track the precession of a black-hole-binary system, using only information from the gravitational-wave (GW) signal. Our method consists of locating the frame from which the magnitude of the $(\ell=2,|m|=2)$ modes is maximized, which we denote the "quadrupole-aligned" frame. We demonstrate the efficacy of this method when applied to waveforms from numerical simulations. In the test case of an equal-mass nonspinning binary, our method locates the direction of the orbital angular momentum to within $(Δθ, Δϕ) = (0.05^{\circ},0.2^{\circ})$. We then apply the method to …
Characteristic precessions of spherical orbit around a rotating braneworld black hole
本研究在Randall-Sundrum框架下分析旋转膜世界黑洞球形轨道的进动，发现潮汐电荷显著改变节点与近星点进动及Lense-Thirring效应，为强场引力测试提供新途径。
Misinterpreting spin precession as orbital eccentricity in gravitational-wave signals
本文研究了引力波信号中自旋进动与偏心率的退相干问题，发现两者存在高度局部化的退相干效应，并对信号长度和倾角敏感。
In the post-Newtonian (PN) regime, the timescale on which the spins of binary black holes precess is much shorter than the radiation-reaction timescale on which the black holes inspiral to smaller separations. On the precession timescale, the angle between the total and orbital angular momenta oscillates with nutation period $τ$, during which the orbital angular momentum precesses about the total angular momentum by an angle $α$. This defines two distinct frequencies that vary on the radiation-reaction timescale: the nutation frequency $ω\equiv 2π/τ$ and the precession frequency $Ω\equiv α/τ$.…
The supermassive black hole (SMBH) with 4 millions solar mass inside the radio-source Sgr A* in our Galactic center is the nearest SMBH. Once the S stars with shorter period are observed, the relativistic precessions especially the Lense-Thirring one can be measured by astronomical observations at 10 micro-arcsecond ($μ$as) level in future. An interesting but so far no attended problem is that the SMBH has not only spin but also spin precession like the other objects in the universe. In this paper, we study the effect of such spin precession on the orbital precessions of orbiting stars. Our re…
Orbital stability, relativistic precession, and QPO constraints for constant-curvature black holes in $f(R)$ gravity
本文在 $f(R)$ 引力常曲率背景下分析轨道稳定性与进动，结合QPO和动力学质量数据给出曲率约束，未发现偏离Kerr的显著证据。
Orbital dynamics and precession in magnetized Kerr spacetime
研究磁化 Kerr 黑洞空间中中性测试粒子的轨道结构与进动动力学，揭示强磁场下轨道运动的临界条件及磁化对强场动力学的影响。
After giving a short overview of previous results on constraining of Extended Gravity (EG) by stellar orbits, we discuss the Schwarzschild orbital precession of S2 star assuming the congruence with predictions of General Relativity (GR). At the moment, the S2 star trajectory is remarkably fitted with the first post-Newtonian (pN) approximation of GR. In particular, both Keck and VLT (GRAVITY) teams declared that the gravitational redshift near its pericenter passage for the S2 star orbit corresponds to theoretical estimates found with the first pN approximation. In 2020, the GRAVITY Collaborat…
Orbital Precession and Hidden Symmetries in Scalar-Tensor Theories
本文将轨道进动、Laplace-Runge-Lenz对称性与振幅t道不连续性相联系，计算标量-张量理论二阶PM势与进动，并利用该对称性自举N=8超引力三圈黑洞散射。
An analysis of all known spherically symmetric solutions to the field equations originating from the Riemann tensor quadratic curvature Lagrangian is presented. A new exact solution is found for the field equation originating from the "energy-momentum" equation of the gauge gravity theory. Imposing equivalence between the Palatini and standard variational field equations yields an algebraic condition that restricts the number spacetime solutions to gauge gravity. An analysis of a new spherically symmetric solution to the conformal gravity field equations is also presented. Point particle orbit…
We use latest data from solar system planetary orbital motions to put constraints on some Galileon-induced precessional effects. Due to the Vainshtein mechanism, the Galileon-type spherically symmetric field of a monopole induces a small, screened correction proprtional to \sqrt{r} to its usual r^-1 Newtonian potential which causes a secular precession of the pericenter of a test particle. In the case of our solar system, latest data from Mars allow to constrain the magnitude of such an interaction down to α<= 0.3 level. Another Galileon-type effect which might impact solar system dynamics is …
Binary-black-hole orbits precess when the black-hole spins are mis-aligned with the binary's orbital angular momentum. The apparently complicated dynamics can in most cases be described as simple precession of the orbital angular momentum about an approximately fixed total angular momentum. However, the imprint of the precession on the observed gravitational-wave signal is yet more complicated, with a non-trivial time-varying dependence on black-hole dynamics, the binary's orientation and the detector polarization. As a result, it is difficult to predict under which conditions precession effec…
We analytically calculate the secular precession of the pericenter of a test particle orbiting a central body surrounded by a continuous distribution of Dark Matter (DM) by using some commonly adopted density profiles for it. We obtain exact expressions without resorting to a-priori simplifying assumptions on the orbital geometry of the test particle. Our formulas allow us to put constraints on the parameters of the DM distributions considered in several local astronomical and astrophysical scenarios, such as the Sun's planetary system, the double pulsar, and the stellar system around the supe…
An elementary pedagogical derivation of the Lense-Thirring precession is given based on the use of Hamilton vector. The Hamilton vector is an extra constant of motion of the Kepler/Coulomb problem related simply to the more popular Runge-Lenz vector. When a velocity-dependent Lorentz-like gravitomagnetic force is present, the Hamilton vector, as well as the canonical orbital momentum are no longer conserved and begin to precess. It is easy to calculate their precession rates, which are related to the Lense-Thirring precession of the orbit.
Synergies in analysing binary black hole mergers: Effect of orbital eccentricity, spin-precession, and non-quadrupole modes
本文研究轨道偏心率、自旋进动与高阶模式在双黑洞引力波数据分析中的协同影响，揭示波形忽略这些效应的偏差，并改进SIQM检验及未来探测需求。
Perihelion precession of planetary orbits solved from quantum field theory
本研究基于纳入引力的扩展标准模型量子场论，通过统一引力狄拉克方程建模电子引力束缚态并取经典极限，推导出与广义相对论一致的行星近日点进动，证明引力量子场论可直接导出相关广义相对论效应。
We study the exact evolution of the orbital angular momentum of a massive particle in the gravitational field of a Kerr black hole. We show analytically that, for a wide class of orbits, the angular momentum's hodograph is always close to a circle. This applies to both bounded and unbounded orbits that do not end up in the black hole. Deviations from the circular shape do not exceed $\approx10\%$ and $\approx7\%$ for bounded and unbounded orbits, respectively. We also find that nutation provides an accurate approximation for those deviations, which fits the exact curve within $\sim 0.01\%$ for…
We use the `moving puncture' approach to perform fully non-linear evolutions of spinning quasi-circular black-hole binaries with individual spins not aligned with the orbital angular momentum. We evolve configurations with the individual spins (parallel and equal in magnitude) pointing in the orbital plane and 45-degrees above the orbital plane. We introduce a technique to measure the spin direction and track the precession of the spin during the merger, as well as measure the spin flip in the remnant horizon. The former configuration completes 1.75 orbits before merging, with the spin precess…
An exact expression derived in the literature for the rate of dragging of inertial frames (Lense-Thirring (LT) precession) in a general stationary spacetime, is reviewed. The exact LT precession frequencies for Kerr, Kerr-Taub-NUT and Taub-NUT spacetimes are explicitly derived. Remarkably, in the case of the zero angular momentum Taub-NUT spacetime, the frame-dragging effect is shown {\it not} to vanish, when considered for spinning test gyroscopes. The result becomes sharper for the case of vanishing ADM mass of that spacetime. We clarify how our results are consistent with claims in the rece…
Effects of orbital precession on hyperbolic encounters
本文研究两个致密天体双曲线交会的动力学，分析轨道进动对引力波暴发射的影响，并提供应变、功率谱模板及记忆效应解析表达式。
We present a reanalysis of GW151226, the second binary black hole merger discovered by the LIGO--Virgo Collaboration. Previous analysis showed that the best-fit waveform for this event corresponded to the merger of a $\sim 14 \, M_\odot$ black hole with a $\sim 7.5 \, M_\odot$ companion, and the posterior distribution in mass ratio ($q \leq 1$) is rather flat. In this work, we perform parameter estimation using a waveform model that includes the effects of orbital precession and higher-order radiative multipole modes, and we find that the source parameters of GW151226 shift towards the low $q$…
A typical stellar mass black hole with a lighter companion is shown to succumb to a chaotic precession of the orbital plane. As a result, the optimal candidates for the direct detection of gravitational waves by Earth based interferometers can show irregular modulation of the waveform during the last orbits before plunge. The precession and the subsequent modulation of the gravitational radiation depends on the mass ratio, eccentricity, and spins. The smaller the mass of the companion, the more prominent the effect of the precession. The most important parameters are the spin magnitudes and mi…
We analyze in detail the spin precession equations in binary black hole systems, when the tidal torque on a Kerr black hole due to quadrupole-monopole coupling is taken into account. We show that completing the precession equations with this term reveals the existence of a conserved quantity at 2PN order when averaging over orbital motion. This quantity allows one to solve the (orbit-averaged) precession equations exactly in the case of equal masses and arbitrary spins, neglecting radiation reaction. For unequal masses, an exact solution does not exist in closed form, but we are still able to …
Measuring the Lense-Thirring Orbital Precession and the Neutron Star Moment of Inertia with Pulsars
本文通过双脉冲星轨道中的Lense-Thirring效应测量中子星转动惯量，以约束方程状态并提升引力测试精度。
New observations of the binary pulsar B1913+16 are presented. Since 1978 the leading component of the pulse profile has weakend dramatically by about 40%. For the first time, a decrease in component separation is observed, consistent with expectations of geodetic precession. Assuming the correctness of general relativity and a circular hollow-cone like beam, a fully consistent model for the system geometry is developed. The misalignment angle between pulsar spin and orbital momentum is determined giving direct evidence for an asymmetric kick during the second supernova explosion. It is argued …
The measurable impact of the 2pN spin-dependent accelerations on the jet precession of M87$^\ast$
研究受黑洞周围盘/喷流共进动测量启发，计算克尔度规中无电荷无自旋物体加速度至二阶后牛顿阶，分析新加速度影响，得出与黑洞角动量相关的轨道进动表达式及参数空间允许域，为相关现象研究提供依据。
The Influence of Stable Photon Sphere Advent on Orbital Precession in moving towards the Extremality
本文通过逐帧绝热近似，研究极端极限下黑洞质量动态变化对试验粒子近心点移动的影响，并探讨其作为弱引力猜想一致性检验的可行性。
Revisiting the Coprecessing Frame in the Presence of Orbital Eccentricity
研究在存在显著轨道偏心率时，耦合进动框架对波形建模的影响，发现尽管波形匹配度有所降低，但仍需进一步改进以提高建模精度。
Can the jet precession of M87$^\ast$ be caused by a distant intermediate-mass black hole?
本文研究了M87*喷流进动是否可能由远处的中等质量黑洞引起，并通过参数空间排除图排除了这种可能性。
Parameter estimation for the GWTC-4.0 catalog with phenomenological waveform models that include orbital eccentricity and an updated description of spin precession
本文利用改进的波形模型对GWTC-4.0目录中的二黑洞并合事件进行参数估计，探讨轨道偏心率和自旋进动对源属性的影响。
Orbital eccentricity in a neutron star - black hole merger
研究通过引力波观测探测中子星-黑洞合并中的轨道偏心率，采用包含自旋诱导轨道进动和偏心率的波形模型，发现偏心率约为0.145，表明偏心形成可能源于动态相互作用而非孤立二体演化。
General relativity predicts that a rotating body produces a frame-dragging (or Lense-Thirring) effect: the orbital plane of a test particle in a non-equatorial orbit precesses about the body's symmetry axis. In this paper we compute the precession frequencies of circular orbits around rapidly rotating neutron stars for a variety of masses and equations of state. The precession frequencies computed are expressed as numerical functions of the orbital frequency observed at infinity. The post-Newtonian expansion of the exact precession formula is examined to identify the relative magnitudes of the…
We have investigated the geodetic precession and the strong gravitational lensing in the slowly-rotating black hole in the dynamical Chern-Simons modified gravity theory. We present the formulas of the orbital period $T$ and the geodetic precession angle $ΔΘ$ for the timelike particles in the circular orbits around the black hole, which shows that the change of the geodetic precession angle with the Chern-Simons coupling parameter $ξ$ is converse to the change of the orbital period with $ξ$ for fixed $a$. We also discuss the effects of the Chern-Simons coupling parameter on the strong gravitat…
The effects of the spin and quadrupole moment of SgrA* on the orbits of S stars
本文研究Sgr A*自旋和四极矩对S星轨道的影响，通过双时间尺度方法推导2PN阶轨道参数表达式，并模拟更接近黑洞的恒星轨道以验证分析预测。
Periastron precession effect of $f$-mode dynamical tides on gravitational waves from eccentric double white dwarfs
针对偏心双白矮星系统，研究动力学潮汐的近星点进动效应，分析共振、混沌等不同情形下的表现及LISA的可探测性，明确不同质量系统中该效应的测量条件。
General-relativistic precession in a black-hole binary
本文报告在引力波信号GW200129中首次测量到强场自旋轨道进动，其速率比弱场测量快十个数量级，且主黑洞可能高自旋，对现有双星形成模型构成挑战。
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