On the impossibility of using the longitude of the ascending node of GP-B for measuring the Lense–Thirring effect

The possibility of analyzing the node 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%. of better. The aliasing effect of the solid Earth and ocean components of the solar K₁ tidal perturbations would make the measurement of the Lense–Thirring effect on the orbit unfeasible. Indeed, the science period of the GP-B mission amounts to almost one year. During this time span the Lense–Thirring shift on the GP-B node would be 164 milliarcseconds (mas), while the tidal perturbations on its node would have a period of the order of 10³ years and amplitudes of the order of 10⁵ mas.     

On measuring gravitomagnetism via spaceborne clocks: a gravitomagnetic clock effect

The difference in the proper azimuthal periods of revolution of two standard clocks in direct and retrograde orbits about a central rotating mass is proportional to J/Mc², where J and M are, respectively, the proper angular momentum and the mass of the source. It is shown that this circumstance is due to a special gravitomagnetic temporal structure around a rotating mass. In connection with this gravitomagnetic clock effect, we explore the possibility of using spaceborne standard clocks for detecting the gravitomagnetic field of the Earth.     

Quadratic Lagrangians and Topology in Gauge Theory Gravity

We consider topological contributions to the action integral in a gauge theory formulation of gravity. Two topological invariants are found and are shown to arise from the scalar and pseudoscalar parts of a single integral. Neither of these action integrals contribute to the classical field equations. An identity is found for the invariants that is valid for non-symmetric Riemann tensors, generalizing the usual GR expression for the topological invariants. The link with Yang–Mills instantons in Euclidean gravity is also explored. Ten independent quadratic terms are constructed from the Riemann tensor, and the topological invariants reduce these to eight possible independent terms for a quadratic Lagrangian. The resulting field equations for the parity non-violating terms are presented. Our derivations of these results are considerably simpler than those found in the literature.     

Generating Functional in CFT and Effective Action for Two-Dimensional Quantum Gravity on Higher Genus Riemann Surfaces

We formulate and solve the analog of the universal Conformal Ward Identity for the stress-energy tensor on a compact Riemann surface of genus g > 1, and present a rigorous invariant formulation of the chiral sector in the induced two-dimensional gravity on higher genus Riemann surfaces. Our construction of the action functional uses various double complexes naturally associated with a Riemann surface, with computations that are quite similar to descent calculations in BRST cohomology theory. We also provide an interpretation of the action functional in terms of the geometry of different fiber spaces over the Teichmüller space of compact Riemann surfaces of genus g > 1. Received: 12 September 1996 / Accepted: 6 January 1997     

Test of the gravitomagnetic field via laser-ranged satellites

We describe a new experiment to measure the gravitomagnetic field of the Earth. This field, a consequence of the general relativistic formulation of Mach's principle (WEM—Wheeler-Einstein-Mach principle), has never been detected. The idea is to measure the Lense-Thirring precession of the nodal lines of two laser-ranged satellites with supplementary inclinations. In this way it is possible to separate the relativistic nodal precession from the classical nodal precession due to the multipole moments of the Earth.     

关于纯引力共形反常

本文采用几何和拓扑的方法,讨论弯曲时空中的纯引力共形反常,并得到了纯引力共形反常的新的表达式αε^abcdΩ_abΛΩ_cd+βε^abcd H_abΛH_cd,其中α,β是任意常数,Ω_ab与H_ab分别是Riemann曲率2-形式与Thomas引入的共形不变曲率2-形式。这里,第一项正比于Euler类,第二项除了包含通常熟知的Wegl张量平方项以外,还含有其它共形不变的不变量。 关键词：     

On purely gravito-magnetic vacuum space-times

It is shown that there are no purely magnetic, vacuum, spacetime metrics where any one of the following conditions holds: (a) the ratio of any two eigenvalues of the Weyl tensor is constant, (b) both of the Riemann principal null directions, defining the time-like blade, are nonrotating, (c) the shear tensor possesses an eigenvector v ^a which is defined by one of the space-like Riemann principal directions, (d) the vorticity is parallel to v ^a , where v ^a is defined by one of the space-like Riemann principal directions.This revised version was published online in April 2005. The publishing date was inserted.     

Lovelock tensor as generalized Einstein tensor

We show that the splitting feature of the Einstein tensor, as the first term of the Lovelock tensor, into two parts, namely the Ricci tensor and the term proportional to the curvature scalar, with the trace relation between them is a common feature of any other homogeneous terms in the Lovelock tensor. Motivated by the principle of general invariance, we find that this property can be generalized, with the aid of a generalized trace operator which we define, for any inhomogeneous Euler–Lagrange expression that can be spanned linearly in terms of homogeneous tensors. Then, through an application of this generalized trace operator, we demonstrate that the Lovelock tensor analogizes the mathematical form of the Einstein tensor, hence, it represents a generalized Einstein tensor. Finally, we apply this technique to the scalar Gauss–Bonnet gravity as an another version of string–inspired gravity. This work was partially supported by a grant from the MSRT/Iran.     

Local gravitomagnetism

In a simple two-body system, we calculate the gravitomagnetic components of the metric in the local quasi-inertial frame of one of the bodies. The local geometry in this frame which is freely falling along the geodesic but is directionally fixed with respect to distant stars is primarily denned by the gravitomagnetic components of the local metric. This metric serves to track down the various contributions from the local and distant source and thus provides further insight to the nature of gravitomagnetism. As a result we show that in the quasi-inertial frame geodetic precession is a gravitomagnetic phenomenon. Furthermore we establish a connection between local gravitomagnetic effects and Einstein's principle of equivalence.     

Spin-Spin Interactions in Gauge Theory of Gravity, Violation of Weak Equivalence Principle and New Classical Test of General Relativity

For a long time, it has been generally believed that spin-spin interactions can only exist in a theory where Lorentz symmetry is gauged, and a theory with spin-spin interactions is not perturbatively renormalizable. But this is not true. By studying the motion of a spinning particle in gravitational field, it is found that there exist spin-spin interactions in gauge theory of gravity. Its mechanism is that a spinning particle will generate gravitomagnetic field in space-time, and this gravitomagnetic field will interact with the spin of another particle, which will cause spin-spin interactions. So, spin-spin interactions are transmitted by gravitational field. The form of spin-spin interactions in post Newtonian approximations is deduced. This result can also be deduced from the Papapetrou equation. This kind of interaction will not affect the renormalizability of the theory. The spin-spin interactions will violate the weak equivalence principle, and the violation effects are detectable. An experiment is proposed to detect the effects of the violation of the weak equivalence principle.     

The dual curvature tensors and dynamics of gravitomagnetic matter

Gravitomagnetic charge that can also be referred to as the dual mass or magnetic mass is the topological charge in gravity theory. A gravitomagnetic monopole at rest can produce a stationary gravitomagnetic field. Due to the topological nature of gravitomagnetic charge, the metric of spacetime where the gravitomagnetic matter is present will be nonanalytic. In this paper both the dual curvature tensors (which can characterize the dynamics of gravitational charge/monopoles) and the antisymmetric gravitational field equation of gravitomagnetic matter are presented. We consider and discuss the mathematical formulation and physical properties of the dual curvature tensors and scalar, antisymmetric source tensors, dual spin connection (including the low‐motion weak‐field approximation), dual vierbein field as well as dual current densities of gravitomagnetic charge. It is shown that the dynamics of gravitomagnetic charge can be founded within the framework of the above dual quantities. In addition, the duality relationship in the dynamical theories between the gravitomagnetic charge (dual mass) and the gravitoelectric charge (mass) is also taken into account in the present paper.     

Generalized uncertainty principle and Hořava–Lifshitz gravity

We explore a connection between generalized uncertainty principle (GUP) and modified Ho?ava–Lifshitz (HL) gravity. The GUP density function may be replaced by the cutoff function for the renormalization group of modified Ho?ava–Lifshitz gravity. We find the GUP-corrected graviton propagators and compare these with tensor propagators in the HL gravity. Two are qualitatively similar, but the p⁵$p^5$-term arisen from Cotton tensor is missed in the GUP-corrected graviton propagator.     

The atom as a probe of curved space-time

A one-electron atom is considered in a general curved space-time. The Hamiltonian of the Dirac equation is written in Fermi normal coordinates, including all interaction terms of first order in the Riemann tensor of the space-time. Expressions are obtained for the shifts in various atomic energy levels caused by the curvature. There is a possibility that these shifts would be observable in the spectrum of hydrogen falling into small black holes (radius about 10^–3 cm) left over from the early universe.This essay received the fifth award from the Gravity Research Foundation for the year 1980.-Ed.Work supported in part by the National Science Foundation.     

Spaces with flat symmetry in poincaré gauge theory of gravity

A Taub space is considered in the Poincare gauge theory of gravity. It is shown that the torsion tensor has four nonvanishing components, which can be split into two independent pairs S₀₁ ⁰, S₀₁ ¹, and S₂₃ ⁰, S₂₃ ¹. The analysis of the gravitational field equations leads to the conclusion that in this case only a flat space-time with torsion is possible, and that its metric coefficients and the components of the torsion tensor are described by a wave equation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 92–98, April, 1990.     

Testing deviations from the inverse square law with a freely falling gravity gradiometer at balloon altitudes

Summary We discuss a null experiment to search for the fifth force at ranges around 10 km. It is proposed to use a three-axis gravity gradiometer to measure the trace of the Earth gravity tensor from a freely falling elevator dropped by a balloon. The main error sources are considered to some extent. Paper presented at the V Cosmic Physics National Conference, S. Miniato, November 27–30, 1990.     

Interaction between gravity and moving superconductors

We propose a unified phenomenological theory to investigate the interaction between arbitrarily moving superconductors and gravitational fields including the Newtonian gravity, gravitational waves, vector transverse gravitoelectric fields, and vector gravitomagnetic fields. In the limit of weak field and low velocity, the expressions for the induced electromagnetic and gravitational fields in the interior of a moving superconductor are obtained. The Meissner effect, London moment, DeWitt effect, effects of gravitational wave on a superconductor, and induced electric fields in the interior of a freely vibrating superconductor are recovered from these two expressions. We demonstrate that the weak equivalence principle is valid in superconductivity, that Newtonian gravity and gravitational waves will penetrate either a moving superconductor or a superconductor at rest, and that a superconductor at rest cannot shield either vector gravitomagnetic fields or vector transverse gravitoelectric fields.     

Classical Gravitational Interactions and Gravitational Lorentz Force

In quantum gauge theory of gravity, the gravitational field is represented by gravitational gauge field. The field strength of gravitational gauge field has both gravitoelectric component and gravitomagnetic component. In classical level, gauge theory of gravity gives classical Newtonian gravitational interactions in a relativistic form. Besides, it gives gravitational Lorentz force, which is the gravitational force on a moving object in gravitomagnetic field. The direction of gravitational Lorentz force is not the same as that of classical gravitational Newtonian force. Effects of gravitational Lorentz force should be detectable, and these effects can be used to discriminate gravitomagnetic field from ordinary electromagnetic magnetic field.     

Reconsiderations on the formulation of general relativity based on Riemannian structures

We prove that some basic aspects of gravity commonly attributed to the modern connection-based approaches, can be reached naturally within the usual Riemannian geometry-based approach, by assuming the independence between the metric and the connection of the background manifold. These aspects are: 1) the BF-like field theory structure of the Einstein–Hilbert action, of the cosmological term, and of the corresponding equations of motion; 2) the formulation of Maxwellian field theories using only the Riemannian connection and its corresponding curvature tensor, and the subsequent unification of gravity and gauge interactions in a four dimensional field theory; 3) the construction of four and three dimensional geometrical invariants in terms of the Riemann tensor and its traces, particularly the formulation of an anomalous Chern–Simons topological model where the action of diffeomorphisms is identified with the action of a gauge symmetry, close to Witten’s formulation of three-dimensional gravity as a Chern–Simon gauge theory. 4) Tordions as propagating and non-propagating fields are also formulated in this approach. This new formulation collapses to the usual one when the metric connection is invoked, and certain geometrical structures very known in the traditional literature can be identified as remanent structures in this collapse.     

Electrical Conductivity in General Relativity

The general relativistic kinetic theory including the effect of a stationary gravitational field is applied to the electromagnetic transport processes in conductors. Then it is applied to derive the general relativistic Ohm's law where the gravitomagnetic terms are incorporated. The total electric charge quantity and charge distribution inside conductors carrying conduction current in some relativistic cases are considered. The general relativistic Ohm's law is applied to predict new gravitomagnetic and gyroscopic effects which can, in principle, be used to detect the Lense-Thirring and rotational fields.