A relativistic positioning system exploiting pulsating sources for navigation across the Solar System and beyond

We introduce an operational approach to the use of pulsating sources, located at spatial infinity, for defining a relativistic positioning and navigation system, based on the use of null four-vectors in a flatMinkowskian spacetime. We describe our approach and discuss the validity of it and of the other approximations we have considered in actual physical situations. As a prototypical case, we show how pulsars can be used to define such a positioning system: the reception of the pulses for a set of different sources whose positions in the sky and periods are assumed to be known allows the determination of the user’s coordinates and spacetime trajectory, in the reference frame where the sources are at rest. In order to confirm the viability of the method, we consider an application example reconstructing the world-line of an idealized Earth in the reference frame of distant pulsars: in particular we have simulated the arrival times of the signals fromfour pulsars at the location of the Parkes radiotelescope in Australia. After pointing out the simplifications we have made, we discuss the accuracy of the method. Eventually, we suggest that the method could actually be used for navigation across the Solar System and be based on artificial sources, rather than pulsars

Gravitomagnetic time-varying effects on the motion of a test particle

We study the effects of a time-varying gravitomagnetic field on the motion of test particles. Starting from recent results, we consider the gravitomagnetic field of a source whose spin angular momentum has a linearly time-varying magnitude. The acceleration due to such a time-varying gravitomagnetic field is considered as a perturbation of the Newtonian motion, and we explicitly evaluate the effects of this perturbation on the Keplerian elements of a closed orbit. The theoretical predictions are compared with actual astronomical and astrophysical scenarios, both in the solar system and in binary pulsars systems, in order to evaluate the impact of these effects on real systems.Comment: 8 pages, RevTeX; revised to match the version accepted for publication in General Relativity and Gravitatio

The Sagnac Effect in curved space-times from an analogy with the Aharonov-Bohm Effect

In the context of the natural splitting, the standard relative dynamics can be expressed in terms of gravito-electromagnetic fields, which allow to formally introduce a gravito-magnetic Aharonov-Bohm effect. We showed elsewhere that this formal analogy can be used to derive the Sagnac effect in flat space-time as a gravito-magnetic Aharonov-Bohm effect. Here, we generalize those results to study the General Relativistic corrections to the Sagnac effect in some stationary and axially symmetric geometries, such as the space-time around a weakly gravitating and rotating source, Kerr space-time, G\"{odel} universe and Schwarzschild space-time.Comment: 14 pages, 1 EPS figure, LaTeX, accepted for publication in General Relativity and Gravitatio

Will the recently approved LARES mission be able to measure the Lense-Thirring effect at 1%?

After the approval by the Italian Space Agency of the LARES satellite, which should be launched at the end of 2009 with a VEGA rocket and whose claimed goal is a about 1% measurement of the general relativistic gravitomagnetic Lense-Thirring effect in the gravitational field of the spinning Earth, it is of the utmost importance to reliably assess the total realistic accuracy that can be reached by such a mission. The observable is a linear combination of the nodes of the existing LAGEOS and LAGEOS II satellites and of LARES able to cancel out the impact of the first two even zonal harmonic coefficients of the multipolar expansion of the classical part of the terrestrial gravitational potential representing a major source of systematic error. While LAGEOS and LAGEOS II fly at altitudes of about 6000 km, LARES will be placed at an altitude of 1450 km. Thus, it will be sensitive to much more even zonals than LAGEOS and LAGEOS II. Their corrupting impact \delta\mu has been evaluated by using the standard Kaula's approach up to degree L=70 along with the sigmas of the covariance matrices of eight different global gravity solutions (EIGEN-GRACE02S, EIGEN-CG03C, GGM02S, GGM03S, JEM01-RL03B, ITG-Grace02s, ITG-Grace03, EGM2008) obtained by five institutions (GFZ, CSR, JPL, IGG, NGA) with different techniques from long data sets of the dedicated GRACE mission. It turns out \delta\mu about 100-1000% of the Lense-Thirring effect. An improvement of 2-3 orders of magnitude in the determination of the high degree even zonals would be required to constrain the bias to about 1-10%.Comment: Latex, 15 pages, 1 table, no figures. Final version matching the published one in General Relativity and Gravitation (GRG

Non-Relativistic Limit of Dirac Equations in Gravitational Field and Quantum Effects of Gravity

Based on unified theory of electromagnetic interactions and gravitational interactions, the non-relativistic limit of the equation of motion of a charged Dirac particle in gravitational field is studied. From the Schrodinger equation obtained from this non-relativistic limit, we could see that the classical Newtonian gravitational potential appears as a part of the potential in the Schrodinger equation, which can explain the gravitational phase effects found in COW experiments. And because of this Newtonian gravitational potential, a quantum particle in earth's gravitational field may form a gravitationally bound quantized state, which had already been detected in experiments. Three different kinds of phase effects related to gravitational interactions are discussed in this paper, and these phase effects should be observable in some astrophysical processes. Besides, there exists direct coupling between gravitomagnetic field and quantum spin, radiation caused by this coupling can be used to directly determine the gravitomagnetic field on the surface of a star.Comment: 12 pages, no figur

Measurement of lipocalin-2 and syndecan-4 levels to differentiate bacterial from viral infection in children with community-acquired pneumonia

BACKGROUND: In this study, we evaluated the lipocalin-2 (LIP2) and syndecan-4 (SYN4) levels in children who were hospitalized for radiologically confirmed CAP in order to differentiate bacterial from viral infection. The results regarding the LIP2 and SYN4 diagnostic outcomes were compared with the white blood cell (WBC) count and C reactive protein (CRP) levels. METHODS: A total of 110 children <14 years old who were hospitalized for radiologically confirmed CAP were enrolled. Serum samples were obtained upon admission and on day 5 to measure the levels of LIP2, SYN4, and CRP as well as the WBC. Polymerase chain reaction of the respiratory secretions and tests on blood samples were performed to detect respiratory viruses, Streptococcus pneumoniae, and Mycoplasma pneumoniae. RESULTS: CAP was considered to be due to a probable bacterial infection in 74 children (67.3 %) and due to a probable viral infection in 16 children (14.5 %). Overall, 84 children (76.4 %) were diagnosed with severe CAP. The mean values of the WBC count and the LIP2 and SYN4 levels did not differ among the probable bacterial, probable viral, and undetermined cases. However, the CRP serum concentrations were significantly higher in children with probable bacterial CAP than in those with probable viral disease (32.2\u2009\ub1\u200955.5 mg/L vs 9.4\u2009\ub1\u200917.0 mg/L, p\u2009<\u20090.05). The WBC count was the best predictor of severe CAP, but the differences among the studied variables were marginal. The WBC count was significantly lower on day 5 in children with probable bacterial CAP (p\u2009<\u20090.01) and in those with an undetermined etiology (p\u2009<\u20090.01). The CRP and LIP2 levels were significantly lower 5 days after enrollment in all of the studied groups, independent of the supposed etiology of CAP (p\u2009<\u20090.01 for all comparisons). No statistically significant variation was observed for SYN4. CONCLUSIONS: Measuring the LIP2 and SYN4 levels does not appear to solve the problem of the poor reliability of routine laboratory tests in defining the etiology and severity of pediatric CAP. Currently, the CRP levels and WBC, when combined with evaluation of clinical data, can be used to limit the overuse of antibiotics as much as possible and to provide the best treatment to the patient

Thermodynamics in f(R)f(R) gravity in the Palatini formalism

We investigate thermodynamics of the apparent horizon in $f(R)$ gravity in the Palatini formalism with non-equilibrium and equilibrium descriptions. We demonstrate that it is more transparent to understand the horizon entropy in the equilibrium framework than that in the non-equilibrium one. Furthermore, we show that the second law of thermodynamics can be explicitly verified in both phantom and non-phantom phases for the same temperature of the universe outside and inside the apparent horizon.Comment: 20 pages, no figure, accepted in JCA

An assessment of Evans' unified field theory I

Evans developed a classical unified field theory of gravitation and electromagnetism on the background of a spacetime obeying a Riemann-Cartan geometry. This geometry can be characterized by an orthonormal coframe theta and a (metric compatible) Lorentz connection Gamma. These two potentials yield the field strengths torsion T and curvature R. Evans tried to infuse electromagnetic properties into this geometrical framework by putting the coframe theta to be proportional to four extended electromagnetic potentials A; these are assumed to encompass the conventional Maxwellian potential in a suitable limit. The viable Einstein-Cartan(-Sciama-Kibble) theory of gravity was adopted by Evans to describe the gravitational sector of his theory. Including also the results of an accompanying paper by Obukhov and the author, we show that Evans' ansatz for electromagnetism is untenable beyond repair both from a geometrical as well as from a physical point of view. As a consequence, his unified theory is obsolete.Comment: 39 pages of latex, modified because of referee report, mistakes and typos removed, partly reformulated, taken care of M.W.Evans' rebutta

The relativistic Sagnac Effect: two derivations

The phase shift due to the Sagnac Effect, for relativistic matter and electromagnetic beams, counter-propagating in a rotating interferometer, is deduced using two different approaches. From one hand, we show that the relativistic law of velocity addition leads to the well known Sagnac time difference, which is the same independently of the physical nature of the interfering beams, evidencing in this way the universality of the effect. Another derivation is based on a formal analogy with the phase shift induced by the magnetic potential for charged particles travelling in a region where a constant vector potential is present: this is the so called Aharonov-Bohm effect. Both derivations are carried out in a fully relativistic context, using a suitable 1+3 splitting that allows us to recognize and define the space where electromagnetic and matter waves propagate: this is an extended 3-space, which we call "relative space". It is recognized as the only space having an actual physical meaning from an operational point of view, and it is identified as the 'physical space of the rotating platform': the geometry of this space turns out to be non Euclidean, according to Einstein's early intuition.Comment: 49 pages, LaTeX, 3 EPS figures. Revised (final) version, minor corrections; to appear in "Relativity in Rotating Frames", ed. G. Rizzi and M.L. Ruggiero, Kluwer Academic Publishers, Dordrecht, (2003). See also http://digilander.libero.it/solciclo

Cartan's spiral staircase in physics and, in particular, in the gauge theory of dislocations

In 1922, Cartan introduced in differential geometry, besides the Riemannian curvature, the new concept of torsion. He visualized a homogeneous and isotropic distribution of torsion in three dimensions (3d) by the "helical staircase", which he constructed by starting from a 3d Euclidean space and by defining a new connection via helical motions. We describe this geometric procedure in detail and define the corresponding connection and the torsion. The interdisciplinary nature of this subject is already evident from Cartan's discussion, since he argued - but never proved - that the helical staircase should correspond to a continuum with constant pressure and constant internal torque. We discuss where in physics the helical staircase is realized: (i) In the continuum mechanics of Cosserat media, (ii) in (fairly speculative) 3d theories of gravity, namely a) in 3d Einstein-Cartan gravity - this is Cartan's case of constant pressure and constant intrinsic torque - and b) in 3d Poincare gauge theory with the Mielke-Baekler Lagrangian, and, eventually, (iii) in the gauge field theory of dislocations of Lazar et al., as we prove for the first time by arranging a suitable distribution of screw dislocations. Our main emphasis is on the discussion of dislocation field theory.Comment: 31 pages, 8 figure