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We study light deflection from a Reissner-Nordstr\"om-de Sitter black hole in the gravitational monopole background. We first calculate the orbit equation and the contribution of the monopole and black hole parameters to the deflection angle up to second-order for the vanishing cosmological constant case using the Rindler-Ishak method. We also obtain the contribution of the cosmological constant to light deflection in this geometry in the weak field limit using the same method., Comment: v2: 10 pages, 2 figures, matches the published version

The gravitational deflection of light has been measured by many experiments, in accordance with the expectations of the theory of general relativity. In articles hal-01756323 and hal-01970150, the research carried out in the quadridimensional Platonic model framework has successively demonstrated the equivalence of the second quantified declination postulate and the conservation of the absolute angular momentum; and then the link between the conservation of energy and quantified variations of absolute time. These effects, both related to the De Broglie mass waves, can be conjugated and lead precisely, in a quantified way, to these relativistic experimental results.; La déflexion gravitationnelle de la lumière a été mesurée par de nombreuses expériences, conformément aux attentes de la théorie de la relativité générale. Dans les articles hal-01739986 et hal-01949616, les recherches menées dans le cadre du modèle quadridimensionnel platonicien ont mis en évidence, successivement, l’équivalence du second postulat de déclinaison quantifiée et de la conservation du moment cinétique ; puis le lien entre la conservation de l’énergie et les variations quantifiées du temps absolu. Ces effets, tous deux liés à l’onde de phase de De Broglie, peuvent être conjugués et conduisent précisément, de façon quantifiée, à ces résultats expérimentaux relativistes.

The articles hal-01970150 and hal-02444592 propose a modeling of various relativistic phenomena from quantified variations of the Platonic absolute time in the presence of a gravitational field. This article aims to restore uniformity of the flow of this time by attributing these apparent variations to deformations of the Platonic space in a fifth spatial dimension. As we will explain, these deformations will thus lead, in a purely geometric way, to a quantified modeling of the relativistic acceleration of gravity., Les articles hal-01949616 et hal-02397067 proposent une modélisation de divers phénomènes relativistes à partir de variations quantifiées du temps absolu platonicien en présence d'un champ gravitationnel. Le présent article vise à rétablir l'uniformité de l'écoulement de ce temps en attribuant ces variations apparentes à des déformations de l'espace platonicien dans une cinquième dimension spatiale. Comme nous allons l'expliquer, ces déformations vont ainsi conduire, de façon purement géométrique, à une modélisation quantifiée de l'accélération relativiste de la pesanteur.

The gravitational deflection of light has been measured by many experiments, in accordance with the expectations of the theory of general relativity. In articles hal-01756323 and hal-01970150, the research carried out in the quadridimensional Platonic model framework has successively demonstrated the equivalence of the second quantified declination postulate and the conservation of the absolute angular momentum; and then the link between the conservation of energy and quantified variations of absolute time. These effects, both related to the De Broglie mass waves, can be conjugated and lead precisely, in a quantified way, to these relativistic experimental results.; La déflexion gravitationnelle de la lumière a été mesurée par de nombreuses expériences, conformément aux attentes de la théorie de la relativité générale. Dans les articles hal-01739986 et hal-01949616, les recherches menées dans le cadre du modèle quadridimensionnel platonicien ont mis en évidence, successivement, l'équivalence du second postulat de déclinaison quantifiée et de la conservation du moment cinétique ; puis le lien entre la conservation de l'énergie et les variations quantifiées du temps absolu. Ces effets, tous deux liés à l'onde de phase de De Broglie, peuvent être conjugués et conduisent précisément, de façon quantifiée, à ces résultats expérimentaux relativistes.

In this letter, we use a recent wormhole solution known as a ringhole [Gonzalez-Diaz, Phys.\ Rev.\ D {\bf 54}, 6122, 1996] to determine the surface topology and the deflection angle of light in the weak limit approximation using the Gauss-Bonnet theorem (GBT). We apply the GBT and show that the surface topology at the wormhole throat is indeed a torus by computing the Euler characteristic number. As a special case of the ringhole solution, one can find the Ellis wormhole which has the surface topology of a 2-sphere at the wormhole throat. The most interesting results of this paper concerns the problem of gravitational deflection of light in the spacetime of a ringhole geometry by applying the GBT to the optical ringhole geometry. It is shown that, the deflection angle of light depends entirely on the geometric structure of the ringhole geometry encoded by the parameters $b_0$ and $a$, being the ringhole throat radius and the radius of the circumference generated by the circular axis of the torus, respectively. As special cases of our general result, the deflection angle by Ellis wormhole is obtained. Finally, we work out the problem of deflection of relativistic massive particles and show that the deflection angle remains unaltered by the speed of the particles., Comment: 7 pages, 1 figure. Published in Universe. Special Issue "Recent Advances in Wormhole Physics"

The observed position of QSOs may vary due to the gravitational deflection by foreground objects. This effect is eminent in the direction of the Galactic Center. To measure the distance to the Galactic Center with the relative error of a few percent, in addition to the astrometric microlensing by individual stars in the Galaxy, the macro lens effect, the collective gravitational deflection by the core and the bulge of the Galaxy must be considered. This effect is important because it has a secular component. Its magnitude is 0.4 micro-as/yr in the case of internal motion of QSOs by the core and reaches 0.6 micro-as/yr in the case of the collective motion produced by both the core and the bulge. The measurement of these effects will provide valuable information on the density and mass function of the Galactic Center., 資料番号: AA0048096002

Due to the development of High accuracy Astrometry, the positional shift of QSO due to gravitational deflection of light will be detectable. We showed that it is feasible to measure the mass of single star by observing the variation of gravitational deflection casused by the orbital motion of the Earth. For a stars within 100pc with an appropriate background source sach as a QSO within 1 arcsecond,their mass can be determined by measuring the deflection shift with the accuracy of 10 micro-arcsec. On the other hand, in the case that relative angular distance between star and QSOs is known by the other observation, the mass of star can be determined by measuring the shift of gravitational deflection of light We show the feasible to measure the mass of single star by VLBI Exploration of Radio Astrometry (VERA) and we show the general probability of the existence of candidate stars and the list of same candidate stars up to now. In the future, almost all stars within 1 arc-second from the QSOs become the candidate stars using a high accurate and a massive scaled data from a satellite such as GAIA. Therefore we propose that QSOs with nearby stars should be monitored for detection of gravitational lens effect for to detect the gravitational lens effect due to stars and MACHOs and the measurement of stellar mass.

Quantum gravity is quite elusive at the experimental level; thus a lot of interest has been raised by recent searches for quantum gravity effects in the propagation of light from distant sources, like gamma ray bursters and active galactic nuclei, and also in earth-based interferometers, like those used for gravitational wave detection. Here we describe a simple heuristic picture of the quantum fluctuations of the gravitational field that we have proposed recently, and show how to use it to estimate quantum gravity effects in interferometers., LaTeX2e, 8 pages, 2 eps figures: Talk presented at QED2000, 2nd Workshop on Frontier Tests of Quantum Electrodynamics and Physics of the Vacuum; included in conference proceedings