Gravitational Energy-Momentum Density in Teleparallel Gravity

In the context of a gauge theory for the translation group, a conserved energy-momentum gauge current for the gravitational field is obtained. It is a true spacetime and gauge tensor, and transforms covariantly under global Lorentz transformations. By rewriting the gauge gravitational field equation in a purely spacetime form, it becomes the teleparallel equivalent of Einstein's equation, and the gauge current reduces to the Møller's canonical energy-momentum density of the gravitational field.

Radiative corrections for the gauged Thirring model in causal perturbation theory

We evaluate the one-loop fermion self-energy for the gauged Thirring model in (2+1) dimensions. with one massive fermion flavor. We do this in the framework of the causal perturbation theory. In contrast to QED3, the corresponding two-point function turns out to be infrared finite on the mass shell. Then, by means of a Ward identity, we derive the on-shell vertex correction and discuss the role played by causality for non-renormalizable theories.

Time analysis for temporary gravitational capture: Satellites of Uranus

We study the problem of gravitational capture in the framework of the Sun-Uranus-particle system. Part of the space of initial conditions is systematically explored, and the duration of temporary gravitational capture is measured. The location and size of different capture-time regions are given in terms of diagrams of initial semimajor axis versus eccentricity. The other initial orbital elements - inclination (i), longitude of the node (Ω), argument of pericenter (ω), and time of pericenter passage (τ) - are first taken to be zero. Then we investigate the cases with ω = 90°, 180°, and 270°. We also present a sample of results for Ω = 90°, considering the cases i = 60°, 120°, 150°, and 180°. Special attention is given to the influence of the initial orbital inclination, taking orbits initially in opposition at pericenter. In this case, the initial inclination is varied from 0° to 180° in steps of 10°. The success of the final stage of the capture problem, which involves the transformation of temporary captures into permanent ones, is highly dependent on the initial conditions associated with the longest capture times. The largest regions of the initial-conditions space with the longest capture times occur at inclinations of 60°-70° and 160°. The regions of possible stability as a function of initial inclination are also delimited. These regions include not only a known set of retrograde orbits, but also a new sort of prograde orbit with inclinations greater than zero.

Energy and angular momentum of the gravitational field in the teleparallel geometry

The Hamiltonian formulation of the teleparallel equivalent of general relativity is considered. Definitions of energy, momentum and angular momentum of the gravitational field arise from the integral form of the constraint equations of the theory. In particular, the gravitational energy-momentum is given by the integral of scalar densities over a three-dimensional spacelike hypersurface. The definition for the gravitational energy is investigated in the context of the Kerr black hole. In the evaluation of the energy contained within the external event horizon of the Kerr black hole, we obtain a value strikingly close to the irreducible mass of the latter. The gravitational angular momentum is evaluated for the gravitational field of a thin, slowly rotating mass shell. © 2002 The American Physical Society.

Gravitational energy of Kerr and Kerr anti-de Sitter space-times in the teleparallel geometry

In the context of the hamiltonian formulation of the teleparallel equivalent of general relativity we compute the gravitational energy of Kerr and Kerr Anti-de Sitter (Kerr-AdS) space-times. The present calculation is carried out by means of an expression for the energy of the gravitational field that naturally arises from the integral form of the constraint equations of the formalism. In each case, the energy is exactly computed for finite and arbitrary spacelike two-spheres, without any restriction on the metric parameters. In particular, we evaluate the energy at the outer event horizon of the black holes. © SISSA/ISAS 2003.

Effects of the eccentricity on the primames in the gravitational capture phenomenon

Gravitational capture is a characteristic of some dynamical systems in celestial mechanics, as in the elliptic restricted three-body problem that is considered in this paper. The basic idea is that a spacecraft (or any particle with negligible mass) can change a hyperbolic orbit with a small positive energy around a celestial body into an elliptic orbit with a small negative energy without the use of any propulsive system. The force responsible for this modification in the orbit of the spacecraft is the gravitational force of the third body involved in the dynamics. In this way, this force is used as a zero cost control, equivalent to a continuous thrust applied in the spacecraft. One of the most important applications of this property is the construction of trajectories to the Moon. The objective of the present paper is to study in some detail the effects of the eccentricity of the primaries in this maneuver.

An interplanetary mission to Neptune system: Gravitational capture and maneuvers around triton

The gravitational capture was initially used to understand the capture of planetary satellites. However, in the 90's decade, this phenomenon was applied in spacecraft trajectories. Belbruno and Miller studied missions in the Earth-Moon system that uses this technique to save fuel during the insertion of the spacecraft in its final orbit around the Moon. Using a parameter defined as twice the two-body energy of the planet-particle system, Yamakawa also studied the gravitational capture in the Earth-Moon system. In the present paper, this technique is used to study a mission that goes to the Neptune system and perform a gravitational capture in the satellite Triton. The results show direct and retrograde trajectories, for different values of the initial conditions.

Gravitational field of a straight cosmic string in the framework of higher-derivative gravity

The gravitational properties of a straight cosmic string are studied in the linear approximation of higher-derivative gravity. These properties are shown to be very different from those found using linearized Einstein gravity: there exists a short range gravitational (anti-gravitational) force in the nonrelativistic limit; in addition, the deflection angle of a light ray moving in a plane orthogonal to the string depends on the impact parameter. © 2008 World Scientific Publishing Company.

Limit cycles for singular perturbation problems via inverse integrating factor

In this paper singularly perturbed vector fields Xε defined in ℝ2 are discussed. The main results use the solutions of the linear partial differential equation XεV = div(Xε)V to give conditions for the existence of limit cycles converging to a singular orbit with respect to the Hausdorff distance. © SPM.

Third-body perturbation in the case of elliptic orbits for the disturbing body

In the present work it is presented a semi-analytical and a numerical study of the perturbation caused in a spacecraft by a third body using a double averaged analytical model with the disturbing function expanded in Legendre polynomials up to the second-order. The important reason for this procedure is to eliminate the terms due to the short time periodic motion of the spacecraft and to show smooth curves for the evolution of the mean orbital elements for a long time period. The aim of this study is to calculate the effect of lunar perturbations on the orbits of spacecrafts that are traveling around the Earth. It is presented an analysis of the stability of a near-circular orbit and a study to know under which conditions this orbit remains near-circular. A study of the equatorial orbits is also performed.

Influence of nonsphericity of planetary satellites and perturbation of the third-body on the artificial satellites motion

Some orbital characteristics of lunar artificial satellites is presented taking into account the perturbation of the third-body in elliptical orbit and the non-uniform distribution of mass of the Moon. We consider the development of the non-sphericity of the Moon in zonal spherical harmonics up to the ninth order and sectorial harmonic C 22 due to the lunar equatorial ellipticity. The motion of the artificial satellite is studied under the single-averaged analytical model. The average is applied to the mean anomaly of the satellite to analyze low-altitude orbits which are of highest importance for future lunar missions. We found families of frozen orbits with long lifetimes for the problem of an orbiter travelling around the Moon.

Effective gravitational equations for f(R) braneworld models

The viability of achieving gravitational consistent braneworld models in the framework of a f(R) theory of gravity is investigated. After a careful generalization of the usual junction conditions encompassing the embedding of the 3-brane into a f(R) bulk, we provide a prescription giving the necessary constraints in order to implement the projected second-order effective field equations on the brane. © 2013 American Physical Society.

Perturbation of a nonautonomous problem in ℝn

In this paper, we prove a stability result about the asymptotic dynamics of a perturbed nonautonomous evolution equation in ℝn governed by a maximal monotone operator. Copyright © 2013 John Wiley & Sons, Ltd. Copyright © 2013 John Wiley & Sons, Ltd.

Dynamical properties for an ensemble of classical particles moving in a driven potential well with different time perturbation

We consider dynamical properties for an ensemble of classical particles confined to an infinite box of potential and containing a time-dependent potential well described by different nonlinear functions. For smooth functions, the phase space contains chaotic trajectories, periodic islands and invariant spanning curves preventing the unlimited particle diffusion along the energy axis. Average properties of the chaotic sea are characterised as a function of the control parameters and exponents describing their behaviour show no dependence on the perturbation functions. Given invariant spanning curves are present in the phase space, a sticky region was observed and show to modify locally the diffusion of the particles. © 2013 Elsevier B.V.

Efeitos de torques gravitacionais na dinâmica de asteróides múltiplos

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)