Scattering of photons by an external gravitational field in the framework of higher-derivative gravity

The scattering of photons by a static gravitational field, treated as an external field, is discussed in the context of gravity with higher derivatives. It is shown that the R-2 sector of the theory does not contribute to the photon scattering, whereas the R-mu nu(2) sector produces dispersive (energy-dependent) photon propagation.

Some remarks on the neutrino oscillation phase in a gravitational field

The weak gravitational field expansion method to account for the gravitationally induced neutrino oscillation effect is critically examined, then it is shown that the splitting of the neutrino phase into a kinematic and a gravitational phase is not always possible because the relativistic factor modifies the particle interference phase splitting condition in a gravitational field.

Duffin-Kemmer-Petiau and Klein-Cordon-Fock equations for electromagnetic, Yang-Mills and external gravitational field interactions: proof of equivalence

Starting from the Generating functional for the Green Function (GF), constructed from the Lagrangian action in the Duffin-Kemmer-Petiau (DKP) theory (L-approach) we strictly prove that the physical matrix elements of the S-matrix in DKP and Klein-Gordon-Fock (KGF) theories coincide in cases of interacting spin O particles with external and quantized Maxwell and Yang-Mills fields and in case of external gravitational field (without or with torsion), For the proof we use the reduction formulas of Lehmann, Symanzik and Zimmermann (LSZ). We prove that many photons and Yang-Mills particles GF coincide in both theories too. (C) 2000 Elsevier B.V. B.V. All rights reserved.

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 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.

Circular, elliptic and oval billiards in a gravitational field

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Gravitational constraints of dS branes in an AdS Einstein-Brans-Dicke bulk

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Photon mass and gravitational deflection

The deflection of a massive photon by an external gravitational field is energy-dependent. Interesting enough, any massive quantum particle, no matter what its spin is, undergoes dispersive deflection in external gravitational fields. Exploiting the dispersive deflection of the quantized massive electromagnetic radiation by the gravitational field of the Sun, we find an upper bound for the photon mass.

Gravitational rainbow of massive particles

Photon propagation is non-dispersive within the context of semiclassical general relativity. What about the remaining massless particles? It can be shown that at the tree level the scattering of massless particles of spin 0, 1/2, 1 or whatever by a static gravitational field generated by a localized source such as the Sun, treated as an external field, is non-dispersive as well. It is amazing, however, that massive particles, regardless of whether they have integral or half-integral spin, experience an energy-dependent gravitational deflection. Therefore, semiclassical general relativity and gravitational rainbows of massive particles can coexist without conflict. We address this issue in this essay.

Gravitational deflection of massive particles in classical and semiclassical general relativity

We calculate the gravitational deflection of massive particles moving with relativistic velocity in the solar system to second post-Newtonian order. For a particle passing close to the Sun with impact parameter b, the deflection in classical general relativity is Phi(C)[GRAPHICS]where v(0) is the particle speed at infinity and M is the Sun's mass. We compute afterwards the gravitational deflection of a spinless neutral particle of mass m in the same static gravitational field as above, treated now as an external field. For a scalar boson with energy E, the deflection in semiclassical general relativity (SGR) is Phisc[GRAPHICS]This result shows that the propagation of the =2E spinless massive boson produces inexorably dispersive effects. It also shows that the semiclassical prediction is always greater than the geometrical one, no matter what the boson mass is. In addition, it is found that SGR predicts a deflection angle of similar to2.6 arcsec for a nonrelativistic spinless massive boson passing at the Sun's limb.

Torsion and the gravitational interaction

By using a nonholonomous-frame formulation of the general covariance principle, seen as an active version of the strong equivalence principle, an analysis of the gravitational coupling prescription in the presence of curvature and torsion is made. The Coupling prescription implied by this principle is found to be always equivalent to that of general relativity, a result that reinforces the completeness of this theory, as well as the teleparallel point of view according to which torsion does not represent additional degrees of freedom for gravity, but simply an alternative way of representing the gravitational field.

Gravitational and quantum bounds on the photon mass

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

The magnetic field of a current carrying cosmic string

The magnetostatic field of an infinite rectilinear current placed in the stationary gravitational field of a rotating cosmic string is found. An interesting aspect of this problem is that although the metric is mathematically very simple, its physical meaning is not trivial. It depends only on topological parameters. So, the cosmic string vacuum space-time is locally equivalent to the Minkowski space-time, but not globally. The calculations are so simple that they can easily be shown in the classroom. © 1997 American Association of Physics Teachers.

Gravitational Lorentz force and the description of the gravitational interaction

In the context of a gauge theory for the translation group, we have obtained, for a spinless particle, a gravitational analogue of the Lorentz force. Then, we have shown that this force equation can be rewritten in terms of magnitudes related to either the teleparallel or the Riemannian structures induced in spacetime by the presence of the gravitational field. In the first case, it gives a force equation, with torsion playing the role of force. In the second, it gives the usual geodesic equation of general relativity. The main conclusion is that scalar matter is able to feel any one of the above spacetime geometries, the teleparallel and the metric ones. Furthermore, both descriptions are found to be completely equivalent in the sense that they give the same physical trajectory for a spinless particle in a gravitational field.