We study gravito-magnetic effects in the Palatini formalism of f(R) gravity. On using the Kerr-de Sitter metric, which is a solution of f(R) field equations, we calculate the impact of f(R) gravity on the gravito-magnetic precession of an orbiting gyroscope. We show that, even though an $f(R)$ contribution is present in principle, its magnitude is negligibly small and far to be detectable in the present (like GP-B) and foreseeable space missions or observational tests around the Earth.
Gravitomagnetism--a motional coupling of matter analogous to the Lorentz force in electromagnetism--has observable consequences for any scenario involving differing mass currents. Examples include gyroscopes located near a rotating massive body, and the interaction of two orbiting bodies. In the former case, the resulting precession of the gyroscope is often called ``frame dragging,'' and is the principal measurement sought by the Gravity Probe-B experiment. The latter case is realized in the earth-moon system, and the effect has in fact been confirmed via lunar laser ranging (LLR) to approxim…
We consider the weak field limit of gravity in the vierbein-Einstein-Palatini formalism, find the action and the equations for perturbations around an arbitrary background, and compare them with the usual metric perturbation equations. We also write the Fierz-Pauli equations for massive gravitons on an arbitrary curved background in this formalism.
We investigate the thick brane model in Palatini $f(\mathcal{R})$ gravity. The brane is generated by a real scalar field with a scalar potential. We solve the system analytically and obtain a series of thick brane solutions for the $f(\mathcal{R})=\mathcal{R}+α\mathcal{R}^2$-brane model. It is shown that tensor perturbations of the metric are stable for $df({\mathcal{R}})/d{\mathcal{R}}>0$. For nonconstant curvature solutions, the graviton zero mode can be localized on the brane, which indicates that the four-dimensional gravity can be recovered on the brane. Mass spectrum of graviton KK modes…
Large scale square ring laser gyros with a length of four meters on each side are approaching a sensitivity of 1x10^-11 rad/s/sqrt(Hz). This is about the regime required to measure the gravitomagnetic effect (Lense Thirring) of the Earth. For an ensemble of linearly independent gyros each measurement signal depends upon the orientation of each single axis gyro with respect to the rotational axis of the Earth. Therefore at least 3 gyros are necessary to reconstruct the complete angular orientation of the apparatus. In general, the setup consists of several laser gyroscopes (we would prefer more…
We consider the Palatini formalism of the Born-Infeld gravity. In the Palatini formalism, the propagating mode is only graviton, whose situation is different from that in the metric formalism. We discuss about the FRW cosmology by using an effective potential. Especially we consider the condition that the bouncing could occur. We also give some speculations about the black hole formation
Using gyroscopes we generalize results, obtained for the gravitomagnetic clock effect in the particular case when the exterior spacetime is produced by a rotating dust cylinder, to the case when the vacuum spacetime is described by the general cylindrically symmetric Lewis spacetime. Results are contrasted with those obtained for the Kerr spacetime.
Newtonian gravity and special relativity combine to produce a gravitomagnetic precession of an orbiting gyroscope that is one fourth as large as predicted by General Relativity. The geodetic effect is the same in both cases.
We review the derivation of the metric for a spinning body of any shape and composition using linearized general relativity theory, and also obtain the same metric using a transformation argument. The latter derivation makes it clear that the linearized metric contains only the Eddington $α$ and $γ$ parameters, so no new parameter is involved in frame-dragging or Lense-Thirring effects. We then calculate the precession of an orbiting gyroscope in a general weak gravitational field, described by a Newtonian potential (the gravito-electric field) and a vector potential (the gravito-magnetic fiel…
We propose an under-ground experiment to detect the general relativistic effects due to the curvature of space-time around the Earth (de Sitter effect) and to rotation of the planet (dragging of the inertial frames or Lense-Thirring effect). It is based on the comparison between the IERS value of the Earth rotation vector and corresponding measurements obtained by a tri-axial laser detector of rotation. The proposed detector consists of six large ring-lasers arranged along three orthogonal axes. In about two years of data taking, the 1% sensitivity required for the measurement of the Lense-Thi…
GINGER (Gyroscopes IN GEneral Relativity), based on an array of large dimension ring laser gyroscopes, is aiming at measuring in a ground laboratory the gravito-electric and gravito-magnetic effects (also known as De Sitter and Lense-Thirrings effect), foreseen by General Relativity. The sensitivity depends on the size of the RLG cavities and the cavity losses, considering the present sensitivity, and assuming the total losses of 6 ppm, with 40m perimeter and 1 day of integration time sensitivity of the order of frad/s is attainable. The construction of GINGER is at present under discussion.
Gravitomagnetic effects originates from the rotation of the source of the gravitational field and from the rotational features of the observers' frame. In recent years, gravitomagnetism has been tested by means of its impact on the precession of LAGEOS orbits and on the precession of spherical gyroscopes in the GP-B experiment. What we suggest here is that light can be used as a probe to test gravitomagnetic effects in an terrestrial laboratory: the proposed detector consists of large ring-lasers arranged along three orthogonal axes.
The two gravitomagnetic effects which influence bodies orbiting around a gravitational source are the geodetic effect and the Lense-Thirring effect. The former describes the precession angle of the axis of a spinning gyroscope while in orbit around a nonrotating gravitational source whereas the latter provides a correction for this angle in the case of a spinning source. In this paper we derive the relevant equations in quadratic gravity and relate them to their equivalents in general relativity. Starting with an investigation into Kepler's third law in quadratic gravity with a scalar field, t…
Gravitomagnetism characterize phenomena in the weak field limit within the context of rotating systems. These are mainly manifested in the geodetic and Lense-Thirring effects. The geodetic effect describes the precession of the spin of a gyroscope in orbit about a massive static central object, while the Lense-Thirring effect expresses the analogous effect for the precession of the orbit about a rotating source. In this work, we explore these effects in the framework of Teleparallel Gravity and investigate how these effects may impact recent and future missions. We find that teleparallel theor…
Gravitomagnetic effects are characterized by two phenomena: first, the geodetic effect which describes the precession of the spin of a gyroscope in a free orbit around a massive object, second, the Lense-Thirring effect which describes the precession of the orbital plane about a rotating source mass. We calculate both these effects in the fourth-order theory of conformal Weyl gravity for the test case of circular orbits. We show that for the geodetic effect a linear term arises which may be interesting for high radial orbits, whereas for the Lense-Thirring effect the additional term has a dimi…
It is known that the metric and Palatini formalisms of gravity theories have their own interesting features but also suffer from some different drawbacks. Recently, a novel gravity theory called hybrid metric-Palatini gravity was put forward to cure or improve their individual deficiencies. The action of this gravity theory is a hybrid combination of the usual Einstein-Hilbert action and a $f(\mathcal{R})$ term constructed by the Palatini formalism. Interestingly, it seems that the existence of a light and long-range scalar field in this gravity may modify the cosmological and galactic dynamic…
In $f(R)$ gravity, the metric, presented in the form of the multipole expansion, for the external gravitational field of a spatially compact supported source up to $1/c^3$ order is provided, where $c$ is the velocity of light in vacuum. The metric consists of General Relativity-like part and $f(R)$ part, where the latter is the correction to the former in $f(R)$ gravity. At the leading pole order, the metric can reduce to that for a point-like or ball-like source. For the gyroscope moving around the source without experiencing any torque, the multipole expansions of its spin's angular velociti…
We consider, in Palatini formalism, a modified gravity of which the scalar field derivative couples to Einstein tensor. In this scenario, Ricci scalar, Ricci tensor and Einstein tensor are functions of connection field. As a result, the connection field gives rise to relation, $h_{μν} = f g_{μν}$ between effective metric, $h_{μν}$ and the usual metric $g_{μν}$ where $f \,=\,1 - κϕ^{,α}ϕ_{,α}/2 $. In FLRW universe, NMDC coupling constant is limited in a range of $ -2/ \dotϕ^{2} < κ\leq \infty $ preserving Lorentz signature of the effective metric. Slowly-rolling regime provides $κ< 0$ forbiddin…
In General Relativity, the rotation of a gravitating body like the Earth influences the motion of orbiting test particles or satellites in a non-Newtonian way. This causes, e.g., a precession of the orbital plane known as the Lense-Thirring effect and a precession of the spin of a gyroscope known as the Schiff effect. Here, we discuss a third effect first introduced by Cohen and Mashhoon called the gravitomagnetic clock effect. It describes the difference in proper time of counterrevolving clocks after a revolution of $2π$. For two clocks on counterrotating equatorial circular orbits around th…
One of the possible low-energy consequences of string theory is the addition of a Chern-Simons term to the standard Einstein-Hilbert action of general relativity. It can be argued that the quintessence field should couple to this Chern-Simons term, and if so, it drives in the linearized theory a parity-violating interaction between the gravito-electric and gravitomagnetic fields. In this paper, the linearized spacetime for Chern-Simons gravity around a massive spinning body is found to include new modifications to the gravitomagnetic field that have not appeared in previous work. The orbits of…
Constraint analysis of the three-dimensional massive gravity, the so- called new massive gravity, is studied in the Palatini formalism. We show that amongst 6 components of the metric, 2 are dynamical, which is compatible with the existence of one vector massive graviton in the linearized theory (Fierz-Pauli theory).
We derive an interacting quintessence model on the framework of a recently introduced new class of geometrical scalar-tensor theories of gravity formulated on a Weyl-Integrable geometry, where the gravitational sector is described by both a scalar and a tensor metric field. By using a Palatini variational principle we construct a scalar-tensor action invariant under the Weyl symmetry group of the background geometry, which in the Einstein-Riemann frame leads to a gravitoelectromagnetic theory. We use the gauge freedom of the theory and the fact that the Weyl scalar field couples with matter fi…
The new theory of Self Creation Cosmology has been shown to yield a concordant cosmological solution that does not require inflation, exotic non-baryonic Dark matter or Dark Energy to fit observational constraints. In vacuo there is a conformal equivalence between this theory and canonical General Relativity and as a consequence an experimental degeneracy exists as the two theories predict identical results in the standard tests. However, there are three definitive experiments that are able to resolve this degeneracy and distinguish between the two theories. Here these standard tests and defin…
We perform a full analytical and numerical treatment, to the first post-Newtonian (1pN) order, of the general relativistic long-term spin precession of an orbiting gyroscope due to the mass quadrupole moment $J_2$ of its primary without any restriction on either the gyro's orbital configuration and the orientation in space of the symmetry axis $\boldsymbol{\hat{k}}$ of the central body. We apply our results to the past spaceborne Gravity Probe B (GP-B) mission by finding a secular rate of its spin's declination $δ$ which may be as large as $\lesssim 30-40\,\mathrm{milliarcseconds\,per\,year\,(…
