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.
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
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 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…
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 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…
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.
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.
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…
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 …
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.
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
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…
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…
Lense-Thirring precession of neutron-star accretion flows: Relativistic versus classical precession
Silesian University in Opava（奥帕瓦西里西亚大学）；Nicolaus Copernicus Astronomical Center of the Polish Academy of Sciences（波兰科学院尼古拉·哥白尼天文学中心）；Astronomical Institute of the Czech Academy of Sciences（捷克科学院天文研究所）
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
