Narrow Results

We solve numerically in the complex plane all the differential equations involved in Hartle's perturbation method for computing general-relativistic polytropic models of rotating neutron stars. We give emphasis on computing quantities describing the geometry of models in rapid rotation. Compared to numerical results obtained by certain sophisticated iterative methods, we verify appreciable improvement of our results vs to those given by the classical Hartle's perturbative scheme.

In this paper, the relation between the modified Lorenz boosts, proposed in the doubly relativity theories and a linear combination of Conformal Group generators in R^1,d-1 is investigated. The introduction of a new generator is proposed in order to deform the Conformal Group to achieve the connection conjectured. The new generator is obtained through a formal dimensional reduction from a free massless particle living in a R^2,d space. Due to this treatment it is possible to say that even DSR theories modify light-cone structure in R^1,d-1, it could remains, in some cases, untouched in R^2,d.

Surprisingly, the relict cosmological constant has a crucial influence on properties of accretion discs orbiting black holes in quasars and active galactic nuclei. We show it by considering basic properties of both the geometrically thin and thick accretion discs in the Kerr–de Sitter black hole (naked-singularity) spacetimes. Both thin and thick discs must have an outer edge allowing outflow of matter into the outer space, located nearby the so-called static radius, where the gravitational attraction of a black hole is balanced by the cosmological repulsion. Jets produced by thick discs can be significantly collimated after crossing the static radius. Extension of discs in quasars is comparable with extension of the associated galaxies, indicating a possibility that the relict cosmological constant puts an upper limit on extension of galaxies.

The phase equivalent relativistic NN potential, which is related by a nonlinear equation to the original nonrelativistic potential, is used to construct the mass operator (rest Hamiltonian) of the 3-nucleon system. Employing the CD Bonn NN potential, the solution of the relativistic 3N Faddeev equation for ³H shows slightly less binding energy than the corresponding nonrelativistic result. The effect of the Wigner spin rotation on the binding is very small.

In 1680, Cassini proposed oval curves as alternative trajectories for the visible planets around the sun. The Cassini ovals were of course overshadowed by the Kepler's first law (1609), namely the planets move around the sun describing conic orbits. Here, we describe the possibility that the Cassini's idea works at larger or smaller scales. Indeed, we consider the Spiric curves (which are a generalization of the Cassini oval) and present the first steps towards a Spiric gravitational theory. We show that from our formalism an ellipse associated with a planet can be obtained as a particular case.

We determine the coefficients of the terms multiplying the gauge fields, gravitational field and cosmological term in a scheme whereby properties are characterized by N anticommuting scalar Grassmann variables. We do this for general N, using analytical methods; this obviates the need for our algebraic computing package which can become quite unwieldy as N is increased.

This paper gives a short review of the status and applications of computer algebra systems for calculations in relativity and gravitation.

In the study of certain noncommutative versions of Minkowski space–time a lot remains to be understood for a satisfactory characterization of their symmetries. Adopting as our case study the κ-Minkowski noncommutative space–time, on which a large literature is already available, we propose a line of analysis of noncommutative-space–time symmetries that relies on the introduction of a Weyl map (connecting a given function in the noncommutative Minkowski with a corresponding function in commutative Minkowski). We provide new elements in favor of the expectation that the commutative-space–time notion of Lie-algebra symmetries must be replaced, in the noncommutative-space–time context, by the one of Hopf-algebra symmetries. While previous studies appeared to establish a rather large ambiguity in the description of the Hopf-algebra symmetries of κ-Minkowski, the approach here adopted reduces the ambiguity to the description of the translation generators, and our results, independently of this ambiguity, are sufficient to clarify that some recent studies which argued for an operational indistinguishability between theories with and without a length-scale relativistic invariant, implicitly assumed that the underlying space–time would be classical. Moreover, while usually one describes theories in κ-Minkowski directly at the level of equations of motion, we explore the nature of Hopf-algebra symmetry transformations on an action.

Observations of the multi-TeV spectra of the Mkn 501 and other nearby BL Lac objects exhibit the high energy cutoffs predicted to be the result of intergalactic annihilation interactions, primarily with IR photons having a flux level as determined by various astronomical observations. After correcting for such intergalactic absorption, these spectra can be explained within the framework of synchrotron self-Compton emission models. Stecker and Glashow have shown that the existence of this annihilation via electron-positron pair production puts strong constraints on Lorentz invariance violaition. Such constraints have important implications for some quantum gravity and large extra dimension models. A much smaller amount of Lorentz invariance violation has potential implications for understanding the spectra of ultrahigh energy cosmic rays.

Investigations of the possibility that some novel "quantum" properties of space–time might induce a Planck-scale modification of the energy/momentum dispersion relation focused at first on scenarios with Planck-scale violations of Lorentz symmetry, with an associated reduced n-parameter (n<6) rotation-boost symmetry group. More recently several studies have also considered the possibility of a "doubly special relativity," in which the modification of the dispersion relation emerges from a framework with both the Planck scale and the speed-of-light scale as characteristic scales of a 6-parameter group of rotation-boost symmetry transformations (a deformation of the Lorentz transformations). For the schemes with broken Lorentz symmetry at the Planck scale there is a large literature on the derivation of experimental limits. Here we show that the analysis of the experimental limits could be significantly different in a doubly-special-relativity framework. We find that the study of photon stability, synchrotron radiation, and threshold conditions for particle production in collision processes, the three contexts which are considered as most promising for constraining the broken-Lorentz-symmetry scenario, should not provide significant constraints on a doubly-special-relativity parameter space. However, certain types of analyses of gamma-ray bursts should be sensitive to the symmetry deformation. A key element of our study is an observation that removes a possible sign ambiguity for the doubly-special-relativity framework. This result also allows us to characterize more sharply the differences between the doubly-special-relativity framework and the framework of κ-Poincaré Hopf algebras, two frameworks which are often confused with each other in the literature.

We examine some alternative possibilities for an action functional for κ-Minkowski noncommutative space–time. Early works on κ-Minkowski focused on κ-Poincaré covariance and the dependence of the action functional on the choice of Weyl map, renouncing to invariance under cyclic permutations of the factors composing the argument of the action functional. It has been recently suggested, focusing on a specific choice of Weyl map and setting aside the issue of κ-Poincaré covariance of the action functional, that a cyclicity-inducing measure could be introduced in implicit form. We provide an explicit formula for (and derivation of) a choice of measure which indeed ensures cyclicity of the action functional. The same choice of measure is applicable to all the most used choices of Weyl map, but we find that this "cyclicity-inducing measure" is not invariant under κ-Poincaré transformations. We also notice that the cyclicity-inducing measure can be straightforwardly derived using a map which connects the κ-Minkowski space–time coordinates and the space–time coordinates of a "canonical" noncommutative space–time, with coordinate-independent commutators.

We consider the consequences of applying general relativity to the description of the dynamics of a galaxy, given the observed flattened rotation curves. The galaxy is modeled as a stationary axially symmetric pressure-free fluid. In spite of the weak gravitational field and the nonrelativistic source velocities, the mathematical system is still seen to be nonlinear. It is shown that the rotation curves for various galaxies as examples are consistent with the mass density distributions of the visible matter within essentially flattened disks. This obviates the need for a massive halo of exotic dark matter. We determine that the mass density for the luminous threshold as tracked in the radial direction is 10^-21.75kg · m^-3 for these galaxies and conjecture that this will be the case for other galaxies yet to be analyzed. We present a velocity dispersion test to determine the extent, if of any significance, of matter that may lie beyond the visible/HI region. This is determined by examining the rotation curves at different galactic latitudes, bringing into consideration the global dynamical structure of the galaxy. The demand for global consistency applies not only to our own but also to all proposed models and theories. Various comments and criticisms from colleagues are addressed.

Raychaudhuri equation is generalized in the parametrized absolute parallelism geometry. This version of absolute parallelism is more general than the conventional one. The generalization takes into account the suggested interaction between the quantum spin of the moving particle and the torsion of the background gravitational field. The generalized Raychaudhuri equation obtained contains some extra terms, depending on the torsion of space–time, that would have some effects on the singularity theorems of general relativity. Under a certain condition, this equation could be reduced to the original Raychaudhuri equation without any need for a vanishing torsion.

We generalize Fermi coordinates, which correspond to an adapted set of coordinates describing the vicinity of an observer's worldline, to the worldsheet of an arbitrary spatial curve in a static spacetime. The spatial coordinate axes are fixed using a covariant Frenet triad so that the metric can be expressed using the curvature and torsion of the spatial curve. As an application of Fermi–Frenet coordinates, we show that they allow covariant inertial forces to be expressed in a simple and physically intuitive way.

We use the dissipative-type theory (DTT) framework to solve for the evolution of conformal fluids in Bjorken and Gubser flows from isotropic initial conditions. The results compare well with both exact and other hydrodynamic solutions in the literature. At the same time, DTTs enforce the Second Law of thermodynamics as an exact property of the formalism, at any order in deviations from equilibrium, and are easily generalizable to more complex situations.

Today, the original Michelson–Morley experiment and its early repetitions at the beginning of the 20th century are considered as a venerable historical chapter for which, at least from a physical point of view, there is nothing more to refine or clarify. The emphasis is now on the modern versions of these experiments, with lasers stabilized by optical cavities, that, apparently, have improved by many orders of magnitude on the limits placed by those original measurements. Though, in those old experiments light was propagating in gaseous systems (air or helium at atmospheric pressure) while now, in modern experiments, light propagates in a high vacuum or inside solid dielectrics. Therefore, in principle, the difference might not depend on the technological progress only but also on the different media that are tested by preventing a straightforward comparison. Starting from this observation, one can formulate a new theoretical scheme where the tiny, irregular residuals observed so far, from Michelson–Morley to the present experiments with optical resonators, point consistently toward the long sought preferred reference frame tight to the Cosmic Microwave Background (CMB). The existence of this scheme, while challenging the traditional ‘null interpretation’, presented in all textbooks and specialized reviews as a self-evident scientific truth, further emphasizes the central role of these experiments for Relativity, Cosmology and Quantum Physics.

We know energy and mass of a particle can be connected by $E=m{c}^2$. What is the physical basis of this relation? Historically, it was thought to be based on the principle of relativity (PR). A careful examination of the literature, however, indicated that this understanding is not true. Einstein did not derive this relation from PR. Instead, his argument was mainly based on thought experiments, which focused on the similarity between radiation and matter. Following this hint, we suspect that the mass–energy equivalence could be based on the quantum property of wave–particle duality. We know photon and electron can behave as a particle as well as a wave. Such a wave property could make the particle behave differently from Newtonian mechanics. Indeed, using a wave model which treats particles as excitations of the vacuum, we show that the mass–energy equivalence relation can be directly derived based on the quantum relations of Planck and de Broglie. This wave hypothesis has several advantages; not only can it explain naturally why particles can be created in the vacuum; it also predicts that a particle cannot travel faster than the speed of light. This hypothesis can also be tested in experiment.

Since 1976 the International Astronomical Union (IAU) has made a series of resolutions on the reference systems and time scales for high precision data processing in the frame- work of general relativity. This article reviews those resolutions that closely relate with the ASTROD project. We give our comments on how to meet the IAU resolutions in the future ASTROD data processing and what kind of works that need to be done further. For example, the self-gravitation terms should be included in the motion equation of the Earth, which is not included in the present DE ephemerides. And the effect of the Sun's figure on the motion of photons should be considered, which is partly neglected in the IAU metric. We also give the metric and the motion equations for both planets and photons in the parameterized post-Newtonian (PPN) formalism. A further improvement of the framework to the second post-Newtonian (2PN) precision would be necessary for the ASTROD project.

Among the possible explanations for the puzzling observations of cosmic rays above the GZK cutoff there is growing interest in the ones that represent kinematical solutions, based either on general formulations of particle physics with small violations of Lorentz symmetry or on a quantum-gravity-motivated scheme for the breakdown of Lorentz symmetry. An unappealing aspect of these cosmic-ray-puzzle solutions is that they require the existence of a preferred class of inertial observers. Here I propose a new kinematical solution of the cosmic-ray puzzle, which does not require the existence of a preferred class of inertial observers. My proposal is a new example of a type of relativistic theories, the so-called "doubly-special-relativity" theories, which have already been studied extensively over the last two years. The core ingredient of the proposal is a deformation of Lorentz transformations in which also the Planck scale E_p (in addition to the speed-of-light scale c) is described as an invariant. Just like the introduction of the invariant c requires a deformation of the Galileian transformations into the Lorentz transformations, the introduction of the invariant E_p requires a deformation of the Lorentz transformations, but there is no special class of inertial observers. The Pierre Auger Observatory and the GLAST space telescope should play a key role in future developments of these investigations. I also emphasize that the doubly-special-relativity theory here proposed, besides providing a solution for the cosmic-ray puzzle, is also the first doubly-special-relativity theory with a natural description of macroscopic bodies, and may find applications in the context of a recently-proposed dark-energy scenario.

The principle of equivalence is shown to extend to situations involving radiation reaction. For example, the Lorentz force law governs the motion of an isolated charge undergoing radiation reaction. In the case of an isolated uncharged particle of small mass, it is the geodesic equation which governs the motion, even when radiation reaction is included. For a local observer to understand such motion he must subtract the singular field of the particle from the actual electromagnetic and gravitational fields he measures. The remaining source-free fields are then used in computing the motion of the particle. With only local measurements, the observer has no knowledge of the existence of radiation and sees no effect which he would be compelled to describe as radiation reaction.