Marcelo Zimbres, Patricio S. Letelier
For stationary axially symmetric spacetimes we find a simple expression for the Lense-Thirring precession in terms of the Ernst potential. This expression is used to compute, in the weak field approximation, the major non-spherical contributions to the precession of a gyroscope orbiting the Earth. We reproduce previously known results and give a new estimation for non-spherical contributions.
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In this paper, we provide a detailed description of our recent analysis and determination of the frame-dragging effect obtained using the nodes of the satellites LAGEOS and LAGEOS 2, in reply to the paper "On the reliability of the so-far performed tests for measuring the Lense-Thirring effect with the LAGEOS satellites" by L. Iorio
We respond to a recent paper by Rindler on the ``Anti--Machian'' nature of the Lense--Thirring effect. We remark that his conclusion depends crucially on the particular formulation of Mach's principle used.
In this brief note we reply to the authors of a recent preprint in which an alleged explicit proposal of using the mean anomaly of the LAGEOS satellites to measure the general relativistic Lense-Thirring effect in the gravitational field of the Earth is attributed to the present author.
We discuss the gravitomagnetic time delay and the Lense-Thirring effect in the context of Brans-Dicke theory of gravity. We compare the theoretical results obtained with those predicted by general relativity. We show that within the accuracy of experiments designed to measure these effects both theories predict essentially the same result.
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.
This submission has been removed because 'G. Felici' is an apparent pseudonym, in violation of arXiv policies.
Exact expression for the Foldy-Wouthuysen Hamiltonian of scalar particles is used for a quantum-mechanical description of the relativistic Lense-Thirring effect. The exact evolution of the angular momentum operator in the Kerr field approximated by a spatially isotropic metric is found. The quantum-mechanical description of the full Lense-Thirring effect based on the Laplace-Runge-Lenz vector is given in the nonrelativistic and weak-field approximation. Relativistic quantum-mechanical equations for the velocity and acceleration operators are obtained. The equation for the acceleration defines …
The standard Lense-Thirring metric is a century-old slow-rotation large-distance approximation to the gravitational field outside a rotating massive body, depending only on the total mass and angular momentum of the source. Although it is not an exact solution to the vacuum Einstein equations, asymptotically the Lense-Thirring metric approaches the Kerr metric at large distances. Herein we shall discuss a specific variant of the standard Lense-Thirring metric, carefully chosen for simplicity, clarity, and various forms of "improved" behaviour, (to be more carefully defined in the body of the a…
We show here that the recent claim of a test of the Lense-Thirring effect with an error of 0.5% using the Mars Global Surveyor is misleading and the quoted error is incorrect by a factor of at least ten thousand. Indeed, the simple error analysis of [1] neglects the role of some important systematic errors affecting the out-of-plane acceleration. The preliminary error analysis presented here shows that even an optimistic uncertainty for this measurement is at the level of, at least, ~ 3026% to ~ 4811%, i.e., even an optimistic uncertainty is about 30 to 48 times the Lense-Thirring effect. In o…
The construction of ready to use templates for gravitational waves from spinning binaries is an important challenge in the investigation of detectable gravitational wave signals. Here we present a method to evaluate the gravitational wave polarization states for inspiralling compact binaries in the extreme mass ratio limit. We discuss the effects caused by the rotation of the central massive object for eccentric orbits in the Lense-Thirring approximation and give the formal expressions of the polarization states including higher order corrections. Our results are in agreement with existing cal…
The orbital Lense-Thirring precession is considered in the context of constraints for weak-field General Relativity involving the cosmological constant $Λ$. It is shown that according to the current accuracy of satellite measurements the obtained error limits for $Λ$ is self-consistent with cosmological observations. The corrections of $Λ$ term are derived for the strong field Lense-Thirring precession i.e. the frame dragging effect and for the nutation. As a result, in the context of recently proposed $Λ$-gravity we obtain constraints for $Λ$ in both relativistic and weak-field limits. Namely…
In this paper, we investigate the properties of the Lense-Thirring precession frequency and periastron precession of the relativistic bound orbits in slowly rotating naked singularity spacetimes. We show that the precession frequencies of a stationary test gyroscope are quite unique in slowly rotating naked singularity spacetimes, and therefore, one can easily distinguish them from the slowly rotating Kerr black hole spacetime. On the other hand, we also show that in slowly rotating Joshi-Malafarina-Narayan (JMN1) naked singularity spacetime, negative precession of the timelike bound orbits is…
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…
We consider bound geodesic orbits of test masses in the exterior gravitational field of a rotating astronomical source whose proper angular momentum varies linearly with time. The linear perturbation approach of Lense and Thirring is herein extended to the nonstationary case. In particular, we investigate the instability of Lense-Thirring precessing orbits due to the slow temporal variation of the gravitomagnetic field of the source.
We investigate the Hamilton-Jacobi equation of a probe particle moving on d-dimensional generalized Lense-Thirring metric. This space-time is different from the slowly rotating Myers-Perry black hole at second order in rotation parameters. We show that the dynamics of the probe particle along the time-like geodesic of the generalized Lense-Thirring space-time is super-integrable and has more constants of motion with respect to the same dynamics on Myers-Perry black hole. We also discuss the second rank Killing tensors associated with the generalized Lense-Thirring metric.
Solar-Limb Effect is an observational phenomena connected to the solar gravitational red-shift. It shows a variation of the magnitude of the gravitational red-shift from the center to the limb of the solar disc. In the present work an attempt, for interpreting this phenomena using a general relativistic red-shift formula, is given . This formula takes into account the effect of the the Sun's gravitational field, the effect of the solar rotation, the effect of inclination of the line of sight and the motion of the observer. In this study the gravitational field of the Sun is assumed to be given…
Recently, the current authors have formulated and extensively explored a rather novel Painleve-Gullstrand variant of the slow-rotation Lense-Thirring spacetime, a variant which has particularly elegant features -- including unit lapse, intrinsically flat spatial 3-slices, and a separable Klein-Gordon equation (wave operator). This spacetime also possesses a non-trivial Killing tensor, implying separability of the Hamilton-Jacobi equation, the existence of a Carter constant, and complete formal integrability of the the geodesic equations. Herein we investigate the geodesics in some detail, in t…
Rotation of a body, according to Einstein's theory of general relativity, generates a "force" on other matter; in Newton's gravitational theory only the mass of a body produces a force. This phenomenon, due to currents of mass, is known as gravitomagnetism owing to its formal analogies with magnetism due to currents of electric charge. Therefore, according to general relativity, Earth's rotation should influence the motion of its orbiting satellites. Indeed, we analysed the laser ranging observations of the orbits of the satellites LAGEOS and LAGEOS II, using a program developed at NASA/GSFC, …
An exact expression of Lense-Thirring precession rate is derived for non-extremal and extremal Plebański-Demiański spacetimes. This formula is used to find the exact Lense-Thirring precession rate in various axisymmetric spacetimes, like: Kerr, Kerr-Newman, Kerr-de Sitter etc. We also show, if the Kerr parameter vanishes in Plebański-Demiański(PD) spacetime, the Lense-Thirring precession does not vanish due to the existence of NUT charge. To derive the LT precession rate in extremal Plebański-Demiański we first derive the general extremal condition for PD spacetimes. This general result could …
The geodesics of bound spherical orbits i.e. of orbits performing Lense-Thirring precession, are obtained in the case of the $Λ$-term within gravito-electromagnetic formalism. It is shown that the presence of the $Λ$-term in the equations of gravity leads to both relativistic and non-relativistic corrections in the equations of motion. The contribution of the $Λ$-term in the Lense-Thirring precession is interpreted as an additional relativistic correction and the gravito-gyromagnetic ratio is defined.
Recently, the authors have formulated and explored a novel Painleve-Gullstrand variant of the Lense-Thirring spacetime, which has some particularly elegant features -- including unit-lapse, intrinsically flat spatial 3-slices, and some particularly simple geodesics, the "rain" geodesics. At linear level in the rotation parameter this spacetime is indistinguishable from the usual slow-rotation expansion of Kerr. Herein, we shall show that this spacetime possesses a nontrivial Killing tensor, implying separability of the Hamilton-Jacobi equation. Furthermore, we shall show that the Klein-Gordon …
The gravitational radiation backreaction effects are considered in the Lense-Thirring approximation. New methods for parameterizing the orbit and for averaging the instantaneous radiative losses are developed. To first order in the spin S of the black hole, both in the absence and in the presence of gravitational radiation, a complete description of the test-particle orbit is given. This is achieved by two improvements over the existing descriptions. First, by introducing new angle variables with a straightforward geometrical meaning. Second, by finding a new parametrization of a generic orbit…
We analyze the influence of the gravitational field produced by a slowly rotating black hole with a cosmic string along the axis of symmetry on a massive scalar field. Exact solutions of both angular and radial parts of the Klein-Gordon equation in this spacetime are obtained, and are given in terms of the confluent Heun functions. We emphasize the role of the presence of the cosmic string in these solutions. We also investigate the solutions in regions near and far from the event horizon. From the radial solution, we obtain the exact wave solutions near the exterior horizon of the black hole,…
The Double Pulsar system PSR J0737-3039A/B has proven to be an excellent laboratory for high precision tests of general relativity. With additional years of timing measurements and new telescopes like the Square Kilometre Array (SKA), the precision of these tests will increase and new effects like the Lense-Thirring precession of the orbit will become measurable. Here, we discuss the prospects of measuring the Lense-Thirring effect and thereby constraining the equations of state at supra-nuclear densities in neutron stars using the Double Pulsar.
In this talk, we review the empirical status for modern gravitational theories with emphases on (i) Equivalence Principles; (ii) Lense-Thirring effects and the implications of Gravity Probe B experiment; (iii) Solar-System Tests of Cosmological Models.
We summarize some critical issues pertaining the tests of the general relativistic Lense-Thirring effect performed by I. Ciufolini and coworkers in the gravitational field of the Earth with the geodetic satellites LAGEOS and LAGEOS II tracked with the Satellite Laser Ranging technique.
In this paper we present a rather extensive error budget for the difference of the perigees of a pair of supplementary SLR satellites aimed to the detection of the Lense-Thirring effect.
The precession of the orbital node of a particle orbiting a rotating mass is known as Lense-Thirring effect (LTE) and is a manifestation of the general relativistic phenomenon of dragging of inertial frames or frame-dragging. The LTE has already been measured by using the node drifts of the LAGEOS satellites and GRACE-based Earth gravity field models with an accuracy of about 10% and will be improved down to a few percent with the recent LARES experiment. The Galileo system will provide 27 new node observables for the LTE estimation and their combination with the LAGEOS and LARES satellites ca…
In this paper we reply to recent claims by Ciufolini and Pavlis about certain aspects of the measurement of the general relativistic Lense-Thirring effect in the gravitational field of the Earth. I) The proposal by such authors of using the existing satellites endowed with some active mechanism of compensation of the non-gravitational perturbations as an alternative strategy to improve the currently ongoing Lense-Thirring tests is unfeasible because of the impact of the uncancelled even zonal harmonics of the geopotential and of some time-dependent tidal perturbations. II) It is shown that the…
The possibility of performing post-Newtonian gravitoelectromagnetic measurements with a joint LAGEOS-LAGEOS II-OPTIS space-based mission is investigated
An exact expression for the rate of dragging of inertial frames (Lense-Thirring (LT) precession) in a general stationary spacetime, is derived without invoking the weak field approximation. This expression, when used for the Kerr metric, leads to the LT precession frequency in the strong gravity regime appropriate to compact gravitating objects like rotating neutron stars and black holes. Numerical values of the precession rate are computed for a few known cases of pulsars (including a double-pulsar) and compared to the precession rates in the weaker gravity regimes of the earth and the sun.
In this paper we analyze quantitatively the concept of LAGEOS--type satellites in critical supplementary orbit configuration (CSOC) which has proven capable of yielding various observables for many tests of General Relativity in the terrestrial gravitational field, with particular emphasis on the measurement of the Lense--Thirring effect.
After an introduction on phenomena due to spin and mass-energy currents on clocks and photons, we review the 1995-2001 measurements of the gravitomagnetic field of Earth and Lense-Thirring effect obtained by analyzing the orbits of the two laser-ranged satellites LAGEOS and LAGEOS II; this method has provided a direct measurement of Earth's gravitomagnetism with accuracy of the order of 20 %. A future accurate measurement of the Lense-Thirring effect, at the level of 1 % accuracy, may include the LARES experiment that will also provide other basic tests of general relativity and gravitation. F…
The possibility of analyzing the node Omega of the GP-B satellite in order to measure also the Lense-Thirring effect on its orbit is examined. This feature is induced by the general relativistic gravitomagnetic component of the Earth gravitational field. The GP-B mission has been launched in April 2004 and is aimed mainly to the measurement of the gravitomagnetic precession of four gyroscopes carried onboard at a claimed accuracy of 1% or better. The aliasing effect of the solid Earth and ocean components of the solar K_1 tidal perturbations would make the measurement of the Lense-Thirring eff…
The Lense--Thirring spacetime describes a 4-dimensional slowly rotating approximate solution of vacuum Einstein equations valid to a linear order in rotation parameter. It is fully characterized by a single metric function of the corresponding static (Schwarzschild) solution. In this paper, we introduce a generalization of the Lense--Thirring spacetimes to the higher-dimensional multiply-spinning case, with an ansatz that is not necessarily fully characterized by a single (static) metric function. This generalization lets us study slowly rotating spacetimes in various higher curvature gravitie…
A new strategy in deriving the Lense-Thirring effect, in the weak field and slow motion approximation of general relativity, on the orbital elements of a test body in the field of different central rotating sources exhibiting axial symmetry is presented. The approach adopted in the present work, in the case of a perfectly spherical source, leads for all the Keplerian orbital elements of the freely falling particle to the well known Lense-Thirring equations. The case of a central nonspherical body is also worked out.
Gravitational effects on neutrino decoherence in Lense-Thirring metric
该研究以Lense-Thirring度规描述的旋转球体引力场为例，在弱场极限下用高斯波包分析引力对中微子波包退相干的作用，发现中微子振荡的特征相干长度会受引力源质量和角速度的非平凡修正，并探讨了实验意义。
We make use of the absence of Lense-Thirring precession of the innermost megamaser clumps around black holes in order to place upper limits on the spin amplitude of seven black holes at the center of megamaser galaxies: NGC 4258, NGC 2273, UGC 3789, NGC 3393, NGC 5495, NGC 5765b, and UGC 6093. The constraints are derived by requiring that the associated precession time-scale be longer than the age of the megamaser clumps, in order to preserve the single-plane geometry of the megamasers.
Herein we explore the non-equatorial constant-$r$ ("quasi-circular") geodesics (both timelike and null) in the Painleve-Gullstrand variant of the Lense-Thirring spacetime recently introduced by the current authors. Even though the spacetime is not spherically symmetric, shells of constant-$r$ geodesics still exist. Whereas the radial motion is (by construction) utterly trivial, determining the allowed locations of these constant-$r$ geodesics is decidedly non-trivial, and the stability analysis is equally tricky. Regarding the angular motion, these constant-$r$ orbits will be seen to exhibit b…
In this letter we further analyze the concept of the use of a pair of identical geodetic satellites placed in identical orbits except for the inclinations which should be supplementary for measuring the Lense-Thirring effect in the terrestrial gravitational field. It turns out that not only the sum of the nodes, as already proposed for the LAGEOS-LARES mission, but also the difference of the perigees could be fruitfully adopted.
This essay presents a new asymmetry that arises from the interplay of charge conjugation and Lense-Thirring effect. When applied to Majorana neutrinos, the effects predicts nu_e <-> overline{nu}_e oscillations in gravitational environments with rotating sources. Parameters associated with astrophysical environments indicate that the presented effect is presently unobservable for solar neutrinos. But, it will play an important role in supernova explosions, and carries relevance for the observed matter-antimatter asymmetry in the universe.
Gravitational orbital Hall effect of vortex light in Lense-Thirring metric
本研究将涡旋光建模为涡旋拉盖尔-高斯电磁波包，在Lense-Thirring度规下求解协变麦克斯韦方程，发现引力轨道霍尔效应的偏离特性与自旋霍尔效应显著不同，揭示了轨道角动量与引力的独特相互作用。
In this paper we investigate the possibility of measuring the post-Newtonian general relativistic gravitomagnetic Lense-Thirring effect in the Jovian system of its Galilean satellites Io, Europa, Ganymede and Callisto in view of recent developments in processing and modelling their optical observations spanning a large time interval (125 years). The present day best observations have an accuracy between several kilometers to few tens of kilometers, which is just the order of magnitude of the Lense-Thirring shifts of the orbits of the Galilean satellites over almost a century. From a comparison…
In this Chapter we deal with the attempts to measure the general relativistic gravitomagnetic Lense-Thirring effect with the Satellite Laser Ranging (SLR) technique applied to the existing LAGEOS and LAGEOS II terrestrial satellites and to the recently approved LARES.
Radio pulsars in short-period eccentric binary orbits can be used to study both gravitational dynamics and binary evolution. The binary system containing PSR J1141$-$6545 includes a massive white dwarf (WD) companion that formed before the gravitationally bound young radio pulsar. We observe a temporal evolution of the orbital inclination of this pulsar that we infer is caused by a combination of a Newtonian quadrupole moment and Lense-Thirring precession of the orbit resulting from rapid rotation of the WD. Lense-Thirring precession, an effect of relativistic frame-dragging, is a prediction o…
The impact of possible a-priori "imprinting" effects of general relativity itself on recent attempts to measure the Lense-Thirring precessions with the LAGEOS satellites orbiting the Earth and the terrestrial geopotential models by the dedicated mission GRACE is investigated. It is analytically shown that general relativity, not explicitly solved for in the GRACE-based models, may "imprint" their even zonal harmonic coefficients J_L at a non-negligible level, given the present-day accuracy in recovering them. This translates into a bias of the LAGEOS-based relativistic tests as large as the Le…
In this paper we discuss and compare a node-only LAGEOS-LAGEOS II combination and a node-only LAGEOS-LAGEOS II-Ajisai-Jason1 combination for the determination of the Lense-Thirring effect. The new combined EIGEN-CG01C Earth gravity model has been adopted. The second combination cancels the first three even zonal harmonics along with their secular variations but introduces the non-gravitational perturbations of Jason1. The first combination is less sensitive to the non-conservative forces but is sensitive to the secular variations of the uncancelled even zonal harmonics of low degree J4 and J6 …
In this paper we critically analyze the so far performed and proposed tests for measuring the general relativistic Lense-Thirring effect in the gravitational field of the Earth with some of the existing accurately tracked artificial satellites. The impact of the 2nd generation GRACE-only EIGEN-GRACE02S Earth gravity model and of the 1st CHAMP+GRACE+terrestrial gravity combined EIGEN-CG01C Earth gravity model is discussed. The role of the proposed LARES is discussed as well.
In this paper we use, in a preliminary way, the recently released EIGEN2 Earth gravity model, which is based on six months of data of CHAMP only, in order to reassess the systematic error due to the mismodelling in the even zonal harmonics of geopotential in the LAGEOS-LAGEOS II Lense-Thirring experiment involving the nodes of both the LAGEOS satellites and the perigee of LAGEOS II. The first results from the GGM01C Earth gravity model including the first GRACE data are very promising.
Up to now attempts to measure the general relativistic Lense-Thirring effect in the gravitational field of Earth have been performed by analyzing a suitable J_2-J_4-free combination of the nodes Omega of LAGEOS and LAGEOS II and the perigee omega of LAGEOS II with the Satellite Laser Ranging technique. The claimed total accuracy is of the order of 20-30%, but, according to some scientists, it could be an optimistic estimate. The main sources of systematic errors are the mismodelling in the even zonal harmonic coefficients J_l of the multipolar expansion of the gravitational potential of Earth …
With quantitative numerical simulations we show that the secular variations of the even zonal harmonics of the geopotential do affect the measurement of the Lense-Thirring effect with the nodes of LAGEOS and LAGEOS II at a \sim 14% level. Thus, the 1-sigma total error in the performed test with the 2nd generation CHAMP-only EIGEN2 Earth gravity model amounts to 51%, contrary to 18% claimed by Ciufolini.
We examine how the new forthcoming Earth gravity models from the CHAMP and, especially, GRACE missions could improve the measurement of the general relativistic Lense-Thirring effect according to the various kinds of observables which could be adopted. In a very preliminary way, we use the recently released EIGEN2 CHAMP-only and GRACE01S GRACE-only Earth gravity models in order to assess the impact of the mismodelling in the even zonal harmonic coefficients of geopotential which represents one of the major sources of systematic errors in this kind of measurement.
The predicted Lense-Thirring perihelion precession of Mercury induced by the Sun's angular momentum through its general relativistic gravitomagnetic field amounts to 2 milliarcseconds per century. It turned out to be compatible with the latest experimental determinations of the supplementary perihelion precession of Mercury with the INPOP15a ephemerides, whose accuracy level has nowadays reached the magnitude of the predicted relativistic effect itself thanks to the analysis of some years of tracking data of the MESSENGER spacecraft, which orbited Mercury from 2011 to 2015. A dedicated analysi…
When a star is tidally disrupted by a supermassive black hole (SMBH), the streams of liberated gas form an accretion disk after their return to pericenter. We demonstrate that Lense-Thirring precession in the spacetime around a rotating SMBH can produce significant time evolution of the disk angular momentum vector, due to both the periodic precession of the disk and the nonperiodic, differential precession of the bound debris streams. Jet precession and periodic modulation of disk luminosity are possible consequences. The persistence of the jetted X-ray emission in the Swift J164449.3+573451 …
The Lense-Thirring effect is currently being measured by means of a combination of the orbital residuals of the nodes of LAGEOS and LAGEOS II and the perigee of LAGEOS II. The total error is of the order of 20%. The most insidious systematic error is due to the mismodelled even zonal harmonics of the geopotential and amounts to 12.9%, according to EGM96 model. The role and the importance of the LAGEOS--LAGEOS II Lense--Thirring experiment is investigated. Using other suitable combinations with orbital elements of the other existing laser-ranged satellites does not yield significative improveme…
Precession and Lense-Thirring effect of hairy Kerr spacetimes
本文研究毛状Kerr时空对测试陀螺仪和吸积盘的参考系拖拽效应，发现黑洞毛抑制进动频率，并利用频率差异区分黑洞与裸奇点，为区分毛状引力理论与广义相对论提供观测依据。
In the context of the currently ongoing efforts to improve the accuracy and reliability of the measurement of the Lense-Thirring effect in the gravitational field of the Earth it has recently been proposed to use the data from the existing spacecraft endowed with some active mechanisms of compensation of the non-gravitational accelerations like GRACE. In this paper we critically discuss this interesting possibility. Unfortunately, it turns out to be unpracticable because of the impact of the uncancelled even zonal harmonic coefficients of the multipolar expansion of the terrestrial gravitation…
In this note we reply to the criticisms by Felici concerning some aspects of the recent frame-dragging test performed by Iorio with the Mars Global Surveyor (MGS) spacecraft in the gravitational field of Mars.
In this note we reply to the criticisms by Sindoni, Paris and Ialongo concerning some aspects of the recent frame-dragging test performed by Iorio with the Mars Global Surveyor (MGS) spacecraft in the gravitational field of Mars.
We discuss the impact of the present-day uncertainties in the recently released CHAMP and/or GRACE Earth gravity models on the measurement of the Lense-Thirring effect with the nodes of the LAGEOS satellites. Also the role of the secular variations Jdots of the even zonal harmonics is quantitatively assessed via numerical simulations and tests. While the systematic error due to the static part of the geopotential ranges from 4% (EIGEN-GRACE02S) to 9% (GGM02S), the impact of the Jdots amounts to 13% over 11 years. This yields a 19% 1-sigma total error in the test recently performed with EIGEN-G…
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