Relativistic Rotation Research Articles

Basic Aspect of Relativistic Rotation: Franklin Rotation of a Sphere

We give a relativistic treatment to the dynamics of spherical bodies rotating at very high speed. It is found that most of the mass of a homogeneous spherical quark with Franklin rotation is due to the relativistic increase of the mass.

Gravitomagnetic effects in the propagation of electromagnetic waves in variable gravitational fields of arbitrary-moving and spinning bodies

The propagation of light in the gravitational field of self-gravitating spinning bodies moving with arbitrary velocities is discussed. The gravitational field is assumed to be ``weak'' everywhere. The equations of motion of a light ray are solved in the first post-Minkowskian approximation which is linear with respect to the universal gravitational constant G. We do not restrict ourselves to the approximation of a gravitational lens so that the solution of light geodesics is applicable for arbitrary locations of the source of light and the observer. This formalism is applied for studying corrections to the Shapiro time delay in binary pulsars caused by the rotation of the pulsar and its companion. We also derive the correction to the light deflection angle caused by the rotation of gravitating bodies in the solar system (Sun, planets) or a gravitational lens. The gravitational shift of frequency due to the combined translational and rotational motions of light-ray-deflecting bodies is analyzed as well. We give a general derivation of the formula describing the relativistic rotation of the plane of polarization of electromagnetic waves (Skrotskii effect). This formula is valid for arbitrary translational and rotational motion of gravitating bodies and greatly extends the results of previous researchers. Finally, we discuss the Skrotskii effect for gravitational waves emitted by localized sources such as a binary system. The theoretical results of this paper can be applied for studying various relativistic effects in microarcsecond space astrometry and developing corresponding algorithms for data processing in space astrometric missions such as FAME, SIM, and GAIA.

Dielectronic recombination of N^{4+}

The dielectronic recombination spectrum of ${\mathrm{N}}^{4+}$ has been measured with high resolution and accuracy. The ${1s}^{2}2p5l$ resonances in the energy range $0--1.6\mathrm{eV}$ were studied in detail. The experimental spectrum is compared with the results from four different calculations. An almost perfect agreement between the experiment and a calculation which combines relativistic many-body perturbation theory and complex rotation is found. The calculation provides accurate spectroscopic data for all fifty ${1s}^{2}2p5l$ states. The literature value for the ${1s}^{2}2p5s$ ${}^{1}P$ energy level is found to be off by more than 0.1 eV.

Formulation for the internal motion of quasiequilibrium configurations in general relativity

We present a formulation for the internal motion of equilibrium configurations with a rotational Killing vector in general relativity. As an approximation, this formulation is applicable to investigation of the internal motion of quasi-equilibrium configurations such as binary neutron stars. Based on this simple formulation, a condition for the general relativistic counter rotation has been obtained, though in the recent work by Bonazzola, Gourgoulhon and Marck, their condition for the counter rotation is not enough to specify the internal velocity field. Under the condition given in this paper, the internal velocity field can be determined completely. Indeed, in the counter-rotating case, we have also derived Poisson equations for the internal velocity, which take tractable forms in numerical implementation.

Propagation-induced Circular Polarisation in Synchrotron Sources

AbstractThe small degree of circular polarisation observed in some synchrotron sources has a frequency dependence that is not consistent with simple predictions based on the intrinsic circular polarisation of synchrotron emission. The suggestion is explored that the circular polarisation arises as a propagation effect within the source. The physical basis of this alternative mechanism is the fact that the natural wave modes of a synchrotron emitting gas are linearly polarised, allowing partial conversion of linear into circular polarisation as in a quarter-wave plate. A relativistic rotation measure (RRM) is defined to characterise the magnitude of this effect.

Relativistic rotation and pulsar electrodynamics

Two illustrative examples are presented as an application of the relativistic rotation transformation and the nonlinear speed-distance relation.

Relativistic model of two-quark composite systems

Relativistic two-particle composite quark systems are described in the framework of the instant form of relativistic quantum mechanics. A correct description of the spin properties of such composite systems, including relativistic spin rotation is obtained.

Variability spectra of orbiting blobs around a black hole

view Abstract Citations (17) References (61) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Variability Spectra of Orbiting Blobs around a Black Hole Bao, G. ; Ostgaard, E. Abstract Variability power spectra of the distribution of orbiting blobs in an optically thick accretion disk around a black hole are investigated by a full relativistic approach. Both the well-known α disks and β disks are considered. The calculations also include the cases when the emitting matter is optically thin or optically thick. The resulting variability spectra are characterized by a power-law shape with flattening frequency at its lower end and a drop-off frequency at its higher end, both corresponding to the borders of blobs distribution in the disk. The frequencies are intrinsic to all sources with an inhomogeneous accretion disk around a black hole, independent of either the specific property of the disk or the nature of the blobs. The drop- off frequency could be an important clue in determining the mass of the central black hole if the distribution of the blobs extends to the last stable circular orbit around a black hole. It may also be taken as evidence for the relativistic rotation of accretion disks around the hole. The average slopes of the observed X-ray power spectra are around -1.5 for both active galactic nuclei and Galactic black hole candidates, suggesting the number density distribution n(r) is proportional to rdelta^ with 0 <= δ <= 1. This may improve our understanding of fluctuations of accretion disks. Publication: The Astrophysical Journal Pub Date: April 1995 DOI: 10.1086/175502 Bibcode: 1995ApJ...443...54B Keywords: Accretion Disks; Black Holes (Astronomy); Clumps; Power Spectra; Relativistic Effects; Variability; Active Galactic Nuclei; Astronomical Models; Density Distribution; Frequency Ranges; Optical Thickness; Astrophysics; ACCRETION; ACCRETION DISKS; BLACK HOLE PHYSICS; GALAXIES: NUCLEI full text sources ADS | data products SIMBAD (7)

Note on Maxwell’s equations in relativistically rotating frames

It is shown that the relativistic rotation transformation of Trocheris and Takeno restores the full Lorentz covariance of electrodynamics, lost in previous investigations using the Galilean rotation transformation along with the Frenet–Serret tetrad associated to the world line of a rotating observer of velocity v=ωΛr; it also recovers, at the approximation of small velocities, the results of the anholonomic approach corresponding to the use of the ‘‘instantaneous’’ Lorentz transformation of Galilean velocity v=ωr (in domains restricted by r&amp;lt;c/ω).

The relativistic rotation transformation and the corotating source model

view Abstract Citations (10) References (12) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS The Relativistic Rotation Transformation and the Corotating Source Model Kichenassamy, S. ; Krikorian, R. A. Abstract The characteristic parameters of pulsars are derived within the framework of the corotating source model, using the relativistic rotation transformation which respects the relativity of simultaneity at a distance, instead of the usual Galilean one which assumes t-prime = t. The resulting nonlinear relation between speed and angular rotation velocity avoids the use of the 'light cylinder' and the difficulties pertaining to it. Publication: The Astrophysical Journal Pub Date: April 1991 DOI: 10.1086/169890 Bibcode: 1991ApJ...371..277K Keywords: Astronomical Models; Pulsars; Relativistic Effects; Stellar Rotation; Computational Astrophysics; Pulsar Magnetospheres; Stellar Radiation; Stellar Spectra; Astrophysics; PULSARS; RELATIVITY full text sources ADS |

Modeling some two-dimensional relativistic phenomena using an educational interactive graphics software

This paper describes several relativistic phenomena in two spatial dimensions that can be modeled using the collision program of Spacetime Software. These include the familiar aberration, the Doppler effect, the headlight effect, and the invariance of the speed of light in vacuum, in addition to the rather unfamiliar effects like the dragging of light in a moving medium, reflection at moving mirrors, Wigner rotation of noncommuting boosts, and relativistic rotation of shrinking and expanding rods. All these phenomena are exhibited by tracings of composite computer printouts of the collision movie. It is concluded that an interactive educational graphics software with pleasing visuals can have considerable investigative power packed within it.

Energy spectrum of the Klein-Gordon equation in Schwarzschild and Kerr fields

We examine the influence of relativistic gravitational effects and rotation of a central body on the structure of the quasidiscrete energy spectrum of a spinless particle in the field of Schwarzschild and Kerr black holes.

Energy spectrum of the dirac equation for the Scharzschild and Kerr fields

We consider the effect of relativistic corrections and rotation of the central body on the structure of the energy spectrum of a particle with spin in the Schwarzchild and Kerr fields. A splitting of levels is obtained, which corresponds to the classical shift of the perihelion of the orbit and precession of the plane of the gravitational spin-orbit interaction and several nonlinear spin effects are calculated.

Physics in rotating frames. I. On uniform rotation about a fixed axis in some holonomic and anholonomic frames

The principle of equivalence of general theory of relativity provides the possibility of studying rotation at uniform rates about a fixed axis with the help of transformation from an inertial laboratory frame to frames having such rotation. Several metrices of such axial rotation, all of which are permitted by the principle of equivalence, have been enlisted and briefly discussed in the paper. Also enlisted are metrices for some types of screw rotation. Anholonomic differentials for relativistic rotation have also been studied with the help of the theory of exterior differential forms for anholonomic objects, and the theory of local inertial orthonormal tetrads for the same rotation.

Study of the two-nucleon mechanism of pion absorption in nuclei: K. Ohta and M. Thies, Natuurkundig Laboratorium der Vrije Universiteit, Amsterdam, The Netherlands, and T.-S. H. Lee, Argonne National Laboratory, Argonne, Illinois 60439

The principle of equivalence of general theory of relativity provides the possibility of studying rotation at uniform rates about a fixed axis with the help of transformation from an inertial laboratory frame to frames having such rotation. Several metrices of such axial rotation, all of which are permitted by the principle of equivalence, have been enlisted and briefly discussed in the paper. Also enlisted are metrices for some types of screw rotation. Anholonomic differentials for relativistic rotation have also been studied with the help of the theory of exterior differential forms for anholonomic objects, and the theory of local inertial orthonormal tetrads for the same rotation.

Relativistic rotation and the anholonomic object

The purpose of this communication is to call attention to the conceptual economy provided by the object of anholonomity for the theory of relativity. This geometric object expresses certain consequences of relativity theory and provides a single, simple framework for discussing a variety of phenomena. It particularly clarifies the description of relativistic rotation. The relativistic rotational transformation of the four coordinate differentials of flat space–time generates a set of anholonomic, or inexact differentials, whose duals are an orthogonal set of basis vectors. How should a rotating observer interpret physical events referred to such orthogonal, but anholonomic frames? The answer to this question rests upon the origin and physical significance of the object of anholonomity. It is demonstrated that not only is the rotational Lorentz transformation an anholonomic transformation, but that the intrinsic anholonomic effects are essential to interpreting rotational phenomena. In particular, the Sagnac effect may be interpreted as the physical manifestation of temporal anholonomity under rotation. The Thomas precession of a reference axis may be interpreted as a consequence of the spatial anholonomity of the rotating frame. Further, the full four-dimensional covariance of Maxwellian electrodynamics, under a relativistic Lorentz rotation, is possible only with the inclusion of anholonomic effects. Schiff attempted to explain the vanishing of the electromagnetic field tensor in the frame of an observer rotating about a charged spherical capacitor, in terms of an interaction with the distant stars. However, if one employs a Lorentzian rotation and the ensuing orthogonal anholonomic reference frames, an explanation is possible without gravitationally induced currents. The anholonomic approach clarifies the distinction between the physically different operations of source rotation and observer rotation in a flat space–time. It is finally concluded that a consistant theory of relativistic rotation, satisfying the principle of general covariance, inherently requires the presence of the object of anholonomity.