Recent Attempts to Measure the General Relativistic Lense-Thirring Effect with Natural and Artificial Bodies in the Solar System
Lorenzo Iorio
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LaTex2e, 31 pages, 1 figure, 14 tables, 115 references. Invited contribution to the Fifth International School on Field Theory and Gravitation, Cuiaba', Mato Grosso, MT, Brasil, April 20-24 2009
According to general relativity, a spinning body of mass M and angular momentum S, like a star or a planet, generates a gravitomagnetic field which induces, among other phenomena, also the Lense-Thirring effect, i.e. secular precessions of the path of a test particle orbiting it. Direct and indisputable tests of such a relativistic prediction are still missing. We discuss some performed attempts to measure it in the gravitational fields of several bodies in the Solar System with natural and artificial objects. The focus is on the realistic evaluation of the impact of some competing classical forces regarded as sources of systematic uncertainties degrading the total accuracy obtainable.
An assessment of the measurement of the Lense-Thirring effect in the Earth gravity field, in reply to: ``On the measurement of the Lense-Thirring effect using the nodes of the LAGEOS satellites, in reply to ``On the reliability of the so far performed tests for measuring the Lense-Thirring effect with the LAGEOS satellites'' by L. Iorio,'' by I. Ciufolini and E. Pavlis
On the Measurement of the Lense-Thirring effect Using the Nodes of the LAGEOS Satellites in reply to "On the reliability of the so-far performed tests for measuring the Lense-Thirring effect with the LAGEOS satellites" by L. Iorio
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.
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…
The impact of the new CHAMP and GRACE Earth gravity models on the measurement of the general relativistic Lense--Thirring effect with the LAGEOS and LAGEOS II satellites
Reply to ``On the Systematic Errors in the Detection of the Lense-Thirring Effect with a Mars Orbiter '', by Giampiero Sindoni, Claudio Paris and Paolo Ialongo
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.
Some comments about a recent paper on the measurement of the general relativistic Lense-Thirring effect in the gravitational field of the Earth with the laser-ranged LAGEOS and LAGEOS II satellites
The meaning of systematic errors, a comment to "Reply to On the Systematic Errors in the Detection of the Lense-Thirring Effect with a Mars Orbiter", by Lorenzo Iorio
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.
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 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…
Some comments on the recent results about the measurement of the Lense-Thirring effect in the gravitational field of the Earth with the LAGEOS and LAGEOS II satellites
Reply to "The meaning of systematic errors, a comment to "Reply to On the Systematic Errors in the Detection of the Lense-Thirring Effect with a Mars Orbiter", by Lorenzo Iorio'', by G. Felici
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.
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…
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…
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…
