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&

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.

Quasiblack holes with pressure: General exact results

A quasiblack hole is an object in which its boundary is situated at a surface called the quasihorizon, defined by its own gravitational radius. We elucidate under which conditions a quasiblack hole can form under the presence of matter with nonzero pressure. It is supposed that in the outer region an extremal quasihorizon forms, whereas inside, the quasihorizon can be either nonextremal or extremal. It is shown that in both cases, nonextremal or extremal inside, a well-defined quasiblack hole always admits a continuous pressure at its own quasihorizon. Both the nonextremal and extremal cases inside can be divided into two situations, one in which there is no electromagnetic field, and the other in which there is an electromagnetic field. The situation with no electromagnetic field requires a negative matter pressure (tension) on the boundary. On the other hand, the situation with an electromagnetic field demands zero matter pressure on the boundary. So in this situation an electrified quasiblack hole can be obtained by the gradual compactification of a relativistic star with the usual zero pressure boundary condition. For the nonextremal case inside the density necessarily acquires a jump on the boundary, a fact with no harmful consequences whatsoever, whereas for the extremal case the density is continuous at the boundary. For the extremal case inside we also state and prove the proposition that such a quasiblack hole cannot be made from phantom matter at the quasihorizon. The regularity condition for the extremal case, but not for the nonextremal one, can be obtained from the known regularity condition for usual black holes.Comment: 18 pages, no figures; improved introduction, added references, calculations better explaine

Cosmological dynamics of fourth order gravity with a Gauss-Bonnet term

We consider cosmological dynamics in fourth order gravity with both $f(R)$ and $\Phi(\mathcal {G})$ correction to the Einstein gravity ($\mathcal{G}$ is the Gauss-Bonnet term). The particular case for which both terms are equally important on power-law solutions is described. These solutions and their stability are studied using the dynamical system approach. We also discuss condition of existence and stability of de Sitter solution in a more general situation of power-law $f$ and $\Phi$.Comment: published version, references update

Maximal Acceleration Is Nonrotating

In a stationary axisymmetric spacetime, the angular velocity of a stationary observer that Fermi-Walker transports its acceleration vector is also the angular velocity that locally extremizes the magnitude of the acceleration of such an observer, and conversely if the spacetime is also symmetric under reversing both t and phi together. Thus a congruence of Nonrotating Acceleration Worldlines (NAW) is equivalent to a Stationary Congruence Accelerating Locally Extremely (SCALE). These congruences are defined completely locally, unlike the case of Zero Angular Momentum Observers (ZAMOs), which requires knowledge around a symmetry axis. The SCALE subcase of a Stationary Congruence Accelerating Maximally (SCAM) is made up of stationary worldlines that may be considered to be locally most nearly at rest in a stationary axisymmetric gravitational field. Formulas for the angular velocity and other properties of the SCALEs are given explicitly on a generalization of an equatorial plane, infinitesimally near a symmetry axis, and in a slowly rotating gravitational field, including the weak-field limit, where the SCAM is shown to be counter-rotating relative to infinity. These formulas are evaluated in particular detail for the Kerr-Newman metric. Various other congruences are also defined, such as a Stationary Congruence Rotating at Minimum (SCRAM), and Stationary Worldlines Accelerating Radially Maximally (SWARM), both of which coincide with a SCAM on an equatorial plane of reflection symmetry. Applications are also made to the gravitational fields of maximally rotating stars, the Sun, and the Solar System.Comment: 64 pages, no figures, LaTeX, Sections 10 and 11 added with applications to maximally rotating stellar models of Cook, Shapiro, and Teukolsky and to the Sun and Solar System with recent data from Pijpers that the Sun has angular momentum 1.80 x 10^{75} = 0.216 M^2 = 47 hectares = 116 acres (with 0.8% uncertainty) and quadrupole moment (2.18 x 10^{-7})MR^2 = 1.60 x 10^{14} m^3 = 3.7 x 10^{117} (with 3% uncertaity), accepted Feb. 27 for Classical and Quantum Gravit

Closed form micro-macro relationships for periodic masonry

The use of theoretical models for providing a constitutive identification of masonry, starting from the individual properties of the phases (i.e. mortar and bricks), constitutes an attractive alternative to costly experimental investigations. In the case of brickwork with periodic texture, the latter issue is tackled resorting to the homogenization theory by Anthoine [1] and solved by means of the finite element method. In order to obtain closed form formulations many authors in literature made simplifying assumptions regarding either the masonry bond, Pande et al. [2], or the joints thickness, Cecchi & Sab [3]. The simplifications adopted turn out to introduce significant errors in the results when either a large difference in stiffness between the phases or a non negligible thickness of the joint are encountered. In the present paper a homogenization procedure is presented, which takes into account the effect of the bond and the Poisson-type interaction between mortar and brick. Assuming a simplified kinematics for the phases belonging to the R.V.E., the so-called localization problem is solved by imposing the minimization of the average internal strain energy. Closed form formulations are then derived for the equivalent in-plane elastic constants of masonry. The expressions found are consistent with those obtained in literature in the limit cases in which masonry is tackled as a stratified medium or where the joints are treated as interfaces. The accuracy of the results is investigated by means of a comparison with finite element analysis. A parametric study, conducted varying the geometries and the mechanical properties of the phases, shows that the error introduced over a very wide range of values for the elastic properties is lower than 8%, meaning that the procedure is ready to be used for non-linear analysis

An Anisotropic Wormhole:TUNNELLING in Time and Space

We discuss the structure of a gravitational euclidean instanton obtained through coupling of gravity to electromagnetism. Its topology at fixed $t$ is $S^1\times S^2$. This euclidean solution can be interpreted as a tunnelling to a hyperbolic space (baby universe) at $t=0$ or alternatively as a static wormhole that joins the two asymptotically flat spaces of a Reissner--Nordstr\"om type solution with $M=0$.Comment: PLAIN-TEX, 16 pages (4 figures not included), Report DFTT 2/9

On the gravitomagnetic effects in cylindrically symmetric spacetimes

Using gyroscopes we generalize results, obtained for the gravitomagnetic clock effect in the particular case when the exterior spacetime is produced by a rotating dust cylinder, to the case when the vacuum spacetime is described by the general cylindrically symmetric Lewis spacetime. Results are contrasted with those obtained for the Kerr spacetime.Comment: 11 pages Latex, to appear in J.Math.Phy

Floating and sinking: the imprint of massive scalars around rotating black holes

We study the coupling of massive scalar fields to matter in orbit around rotating black holes. It is generally expected that orbiting bodies will lose energy in gravitational waves, slowly inspiralling into the black hole. Instead, we show that the coupling of the field to matter leads to a surprising effect: because of superradiance, matter can hover into "floating orbits" for which the net gravitational energy loss at infinity is entirely provided by the black hole's rotational energy. Orbiting bodies remain floating until they extract sufficient angular momentum from the black hole, or until perturbations or nonlinear effects disrupt the orbit. For slowly rotating and nonrotating black holes floating orbits are unlikely to exist, but resonances at orbital frequencies corresponding to quasibound states of the scalar field can speed up the inspiral, so that the orbiting body "sinks". These effects could be a smoking gun of deviations from general relativity.Comment: 5 pages, two figures, RevTeX4.1. v2: Published in Physical Review Letter

Reheating after f(R) inflation

The reheating dynamics after the inflation induced by $R^2$-corrected $f(R)$ model is considered. To avoid the complexity of solving the fourth order equations, we analyze the inflationary and reheating dynamics in the Einstein frame and its analytical solutions are derived. We also perform numerical calculation including the backreaction from the particle creation and compare the results with the analytical solutions. Based on the results, observational constraints on the model are discussed.Comment: 16 pages, 11 figure