307 research outputs found

### Satellite gravitational orbital perturbations and the gravitomagnetic clock effect

In order to detect the gravitomagnetic clock effect by means of two
counter-orbiting satellites placed on identical equatorial and circular orbits
around the Earth with radius 7000 km their radial and azimuthal positions must
be known with an accuracy of delta r =10^{-1} mm and delta phi =10^{-2} mas per
revolution. In this work we investigate if the radial and azimuthal
perturbations induced by the dynamical and static parts of the Earth' s
gravitational field meet this requirements. While the radial direction is
affected only by harmonic perturbations with periods up to some tens of days,
the azimuthal location is perturbed by a secular drift and very long period
effects.It results that the present level of accuracy in the knowledge both of
the Earth solid and ocean tides, and of the static part of the geopotential
does not allow an easy detection of the gravitomagnetic clock effect, at least
by using short arcs only.Comment: 18 pages, 4 figures. Submitted to Int. Journal of Mod. Phys.

### A Gravitomagnetic Effect on the Orbit of a Test Body due to the Earth's Variable Angular Momentum

The well known general relativistic Lense-Thirring drag of the orbit of a
test particle in the stationary field of a central slowly rotating body is
generated, in the weak-field and slow-motion approximation of General
Relativity, by a gravitomagnetic Lorentz-like acceleration in the equations of
motion of the test particle. In it the gravitomagnetic field is due to the
central body's angular momentum supposed to be constant. In the context of the
gravitational analogue of the Larmor theorem, such acceleration looks like a
Coriolis inertial term in an accelerated frame. In this paper the effect of the
variation in time of the central body's angular momentum on the orbit of a test
mass is considered. It can be shown that it is analogue to the inertial
acceleration due to the time derivative of the angular velocity vector of an
accelerated frame. The possibility of detecting such effect in the
gravitational field of the Earth with LAGEOS-like satellites is investigated.
It turns out that the orbital effects are far too small to be measured.Comment: LaTex2e, 1 table, no figures, 7 page

### MEASURING GRAVITOMAGNETIC EFFECTS BY MEANS OF RING LASERS

Light is a good probe for general relativistic effects. Exploiting the asymmetry of the propagation in the vicinity of a central rotating mass it is possible to use a ring laser in order to measure the frame dragging of the reference frames by the gravitational field of the Earth (Lense-Thirring effect). I shall present the G-GranSasso experiment whose objective is precisely to measure the Lense-Thirring and the de Sitter effects in a terrestrial laboratory. The experimental apparatus will be made of a set of at least three, differently oriented, ring lasers rigidly attached to a central "monument". The signal will be in the form of the beat frequency produced in the annular cavity of each laser by the rotational anisotropy. The laboratory will be located underground in the Laboratori Nazionali del Gran Sasso facility, in Italy. The required sensitivity is just one order of magnitude below the performance of the best existing instruments and the new design will attain i

### Can Solar System observations tell us something about the cosmological constant?

In this note we show that the latest determinations of the residual Mercury's
perihelion advance, obtained by accounting for almost all known Newtonian and
post-Newtonian orbital effects, yields only very broad constraints on the
cosmological constant. Indeed, from \delta\dot\omega=-0.0036 + - 0.0050
arcseconds per century one gets -2 10^-34 km^-2 < Lambda < 4 10^-35 km^-2. The
currently accepted value for Lambda, obtained from many independent
cosmological and large-scale measurements, amounts to almost 10^-46 km^-2.Comment: Latex2e, 4 pages, 2 table, no figures, 11 references. Table 2 added,
typos in the units of Lambda correcte

### Gravitomagnetic time delay and the Lense-Thirring effect in Brans-Dicke theory of gravity

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.Comment: 10 pages Typeset using REVTE

### Trajectory of test particle around a slowly rotating relativistic star emitting isotropic radiation

We explored the motion of test particles near slowly rotating relativistic
star having a uniform luminosity. In order to derive the test particle's
equations of motion, we made use of the radiation stress-energy tensor first
constructed by Miller and Lamb \cite{ML96}. From the particle's trajectory
obtained through the numerical integration of the equations of motion, it is
found that for sufficiently high luminosity, "suspension orbit" exists, where
the test particle hovers around at uniform angular velocity in the same
direction as the star's spin. Interestingly, it turned out that the radial
position of the "suspension orbit" was determined by the luminosity and the
angular momentum of the star alone and was independent of the initial positions
and the specific angular momentum of the particle. Also found is that there
exist not only the radiation drag but also "radiation counter-drag" which
depends on the stellar radius and the angular momentum and it is this radiation
counter-drag that makes the test particle in the "suspension orbit" to hover
around at uniform angular velocity which is greater than that induced by the
Lense-Thirring effect (i.e., general relativistic dragging of inertial frame).Comment: 23 pages, 7 figures, to appear in Phys. Rev. D

### The Principle of Relativity and Inertial Dragging

Machs principle and the principle of relativity have been discussed by H. I.
Hartman and C. Nissim-Sabat in this journal. Several phenomena were said to
violate the principle of relativity as applied to rotating motion. These claims
have recently been contested. However, in neither of these articles have the
general relativistic phenomenon of inertial dragging been invoked, and no
calculation have been offered by either side to substantiate their claims. Here
I discuss the possible validity of the principle of relativity for rotating
motion within the context of the general theory of relativity, and point out
the significance of inertial dragging in this connection. Although my main
points are of a qualitative nature, I also provide the necessary calculations
to demonstrate how these points come out as consequences of the general theory
of relativityComment: 17 page

### The Lense-Thirring effect in the Jovian system of the Galilean satellites and its measurability

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 between analytical
development and numerical integration it turns out that, unfortunately, most of
the secular component of the gravitomagnetic signature is removed in the
process of fitting the initial conditions. Indeed, an estimation of the
magnitude of the Lense-Thirring effect in the ephemerides residuals is given;
the resulting residuals have a maximum magnitude of 20 meters only (over 125
years).Comment: Latex, 10 pages, 4 tables, 3 figures, 27 references. Invited paper
for a Special Issue of Int. J. Mod. Phys. D on the Lense-Thirring effect, D.
Grumiller edito

### On the backreaction of frame dragging

The backreaction on black holes due to dragging heavy, rather than test,
objects is discussed. As a case study, a regular black Saturn system where the
central black hole has vanishing intrinsic angular momentum, J^{BH}=0, is
considered. It is shown that there is a correlation between the sign of two
response functions. One is interpreted as a moment of inertia of the black ring
in the black Saturn system. The other measures the variation of the black ring
horizon angular velocity with the central black hole mass, for fixed ring mass
and angular momentum. The two different phases defined by these response
functions collapse, for small central black hole mass, to the thin and fat ring
phases. In the fat phase, the zero area limit of the black Saturn ring has
reduced spin j^2>1, which is related to the behaviour of the ring angular
velocity. Using the `gravitomagnetic clock effect', for which a universality
property is exhibited, it is shown that frame dragging measured by an
asymptotic observer decreases, in both phases, when the central black hole mass
increases, for fixed ring mass and angular momentum. A close parallelism
between the results for the fat phase and those obtained recently for the
double Kerr solution is drawn, considering also a regular black Saturn system
with J^{BH}\neq 0.Comment: 18 pages, 8 figure

### Frame dragging and super-energy

We show that the vorticity appearing in stationary vacuum spacetimes is
always related to the existence of a flow of super-energy on the plane
orthogonal to the vorticity vector. This result, toghether with the previously
established link between vorticity and super--energy in radiative (Bondi-Sachs)
spacetimes strength further the case for this latter quantity as the cause of
frame dragging.Comment: 12 pages Latex. To appear in Phys.Rev. D. Typos correcte

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