A general relativistic model for the light propagation in the gravitational field of the Solar System: the dynamical case

Modern astrometry is based on angular measurements at the micro-arcsecond level. At this accuracy a fully general relativistic treatment of the data reduction is required. This paper concludes a series of articles dedicated to the problem of relativistic light propagation, presenting the final microarcsecond version of a relativistic astrometric model which enable us to trace back the light path to its emitting source throughout the non-stationary gravity field of the moving bodies in the Solar System. The previous model is used as test-bed for numerical comparisons to the present one. Here we also test different versions of the computer code implementing the model at different levels of complexity to start exploring the best trade-off between numerical efficiency and the micro-arcsecond accuracy needed to be reached.Comment: 40 pages, 5 figures. Accepted for publication on The Astrophysical Journal. Manuscript prepared with AASLaTeX macros v.5.

Testing general relativity by micro-arcsecond global astrometry

The global astrometric observations of a GAIA-like satellite were modeled within the PPN formulation of Post-Newtonian gravitation. An extensive experimental campaign based on realistic end-to-end simulations was conducted to establish the sensitivity of global astrometry to the PPN parameter \gamma, which measures the amount of space curvature produced by unit rest mass. The results show that, with just a few thousands of relatively bright, photometrically stable, and astrometrically well behaved single stars, among the ~10^9 objects that will be observed by GAIA, \gamma can be estimated after 1 year of continuous observations with an accuracy of ~10^{-5} at the 3\sigma level. Extrapolation to the full 5-year mission of these results based on the scaling properties of the adjustment procedure utilized suggests that the accuracy of \simeq 2x10^{-7}, at the same 3\sigma level, can be reached with \~10^6 single stars, again chosen as the most astrometrically stable among the millions available in the magnitude range V=12-13. These accuracies compare quite favorably with recent findings of scalar-tensor cosmological models, which predict for \gamma a present-time deviation, |1-\gamma|, from the General Relativity value between 10^{-5} and 10^{-7}.Comment: 7 pages, 2 figures, to be published in A&

The Formation of non-Keplerian Rings of Matter about Compact Stars

The formation of energetic rings of matter in a Kerr spacetime with an outward pointing acceleration field does not appear to have previously been noted as a relativistic effect. In this paper we show that such rings are a gravimagneto effect with no Newtonian analog, and that they do not occur in the static limit. The energy efficiency of these rings can, depending of the strength of the acceleration field, be much greater than that of Keplerian disks. The rings rotate in a direction opposite to that of compact star about which they form. The size and energy efficiency of the rings depend on the fundamental parameters of the spacetime as well as the strength the acceleration field.Comment: 19 pages, 7 figures, 1 diagram. Figures are included in the text using the "graphicx" package. If you do not have this package you can use epsfig, or another package as long as you alter the tex file appropriately. Alternatively you could print the figures out seperatel

Collimation of a spherical collisionless particles stream in Kerr space-time

We examine the propagation of collisionless particles emitted from a spherical shell to infinity. The number distribution at infinity, calculated as a function of the polar angle, exhibits a small deviation from uniformity. The number of particles moving from the polar region toward the equatorial plane is slightly larger than that of particles in the opposite direction, for an emission radius $> 4.5M$ in extreme Kerr space-time. This means that the black hole spin exerts an anti-collimation effect on the particles stream propagating along the rotation axis. We also confirm this property in the weak field limit. The quadrupole moment of the central object produces a force toward the equatorial plane. For a smaller emission radius $r<4.5M$, the absorption of particles into the black hole, the non-uniformity and/or the anisotropy of the emission distribution become much more important.Comment: 11 pages, 8 figures; accepted for publication in CQ

Modified Special Relativity on a fluctuating spacetime

It was recently proposed that deformations of the relativistic symmetry, as those considered in Deformed Special Relativity (DSR), can be seen as the outcome of a measurement theory in the presence of non-negligible (albeit small) quantum gravitational fluctuations [1,2]. In this paper we explicitly consider the case of a spacetime described by a flat metric endowed with stochastic fluctuations and, for a free particle, we show that DSR-like nonlinear relations between the spaces of the measured and classical momenta, can result from the average of the stochastic fluctuations over a scale set be the de Broglie wavelength of the particle. As illustrative examples we consider explicitly the averaging procedure for some simple stochastic processes and discuss the physical implications of our results.Comment: 7 pages, no figure

Navigation in Curved Space-Time

A covariant and invariant theory of navigation in curved space-time with respect to electromagnetic beacons is written in terms of J. L. Synge's two-point invariant world function. Explicit equations are given for navigation in space-time in the vicinity of the Earth in Schwarzschild coordinates and in rotating coordinates. The restricted problem of determining an observer's coordinate time when their spatial position is known is also considered

Raychaudhuri's equation and aspects of relativistic charged collapse

We use the Raychaudhuri equation to probe certain aspects related to the gravitational collapse of a charged medium. The aim is to identify the stresses the Maxwell field exerts on the fluid and discuss their potential implications. Particular attention is given to those stresses that resist contraction. After looking at the general case, we consider the two opposite limits of poor and high electrical conductivity. In the former there are electric fields but no currents, while in the latter the situation is reversed. When the conductivity is low, we find that the main agents acting against the collapse are the Coulomb forces triggered by the presence of an excess charge. At the ideal Magnetohydrodynamic (MHD) limit, on the other hand, the strongest resistance seems to come from the tension of the magnetic forcelines. In either case, we discuss whether and how the aforementioned resisting stresses may halt the contraction and provide a set of conditions making this likely to happen.Comment: Revised version, to appear in PR

Destroying black holes with test bodies

If a black hole can accrete a body whose spin or charge would send the black hole parameters over the extremal limit, then a naked singularity would presumably form, in violation of the cosmic censorship conjecture. We review some previous results on testing cosmic censorship in this way using the test body approximation, focusing mostly on the case of neutral black holes. Under certain conditions a black hole can indeed be over-spun or over-charged in this approximation, hence radiative and self-force effects must be taken into account to further test cosmic censorship.Comment: Contribution to the proceedings of the First Mediterranean Conference on Classical and Quantum Gravity (talk given by T. P. S.). Summarizes the results of Phys. Rev. Lett. 103, 141101 (2009), arXiv:0907.4146 [gr-qc] and considers further example