167 research outputs found
Relativistic Dyson Rings and Their Black Hole Limit
In this Letter we investigate uniformly rotating, homogeneous and
axisymmetric relativistic fluid bodies with a toroidal shape. The corresponding
field equations are solved by means of a multi-domain spectral method, which
yields highly accurate numerical solutions. For a prescribed, sufficiently
large ratio of inner to outer coordinate radius, the toroids exhibit a
continuous transition to the extreme Kerr black hole. Otherwise, the most
relativistic configuration rotates at the mass-shedding limit. For a given
mass-density, there seems to be no bound to the gravitational mass as one
approaches the black-hole limit and a radius ratio of unity.Comment: 13 pages, 1 table, 5 figures, v2: some discussion and two references
added, accepted for publication in Astrophys. J. Let
Finsler and Lagrange Geometries in Einstein and String Gravity
We review the current status of Finsler-Lagrange geometry and
generalizations. The goal is to aid non-experts on Finsler spaces, but
physicists and geometers skilled in general relativity and particle theories,
to understand the crucial importance of such geometric methods for applications
in modern physics. We also would like to orient mathematicians working in
generalized Finsler and Kahler geometry and geometric mechanics how they could
perform their results in order to be accepted by the community of ''orthodox''
physicists.
Although the bulk of former models of Finsler-Lagrange spaces where
elaborated on tangent bundles, the surprising result advocated in our works is
that such locally anisotropic structures can be modelled equivalently on
Riemann-Cartan spaces, even as exact solutions in Einstein and/or string
gravity, if nonholonomic distributions and moving frames of references are
introduced into consideration.
We also propose a canonical scheme when geometrical objects on a (pseudo)
Riemannian space are nonholonomically deformed into generalized Lagrange, or
Finsler, configurations on the same manifold. Such canonical transforms are
defined by the coefficients of a prime metric and generate target spaces as
Lagrange structures, their models of almost Hermitian/ Kahler, or nonholonomic
Riemann spaces.
Finally, we consider some classes of exact solutions in string and Einstein
gravity modelling Lagrange-Finsler structures with solitonic pp-waves and
speculate on their physical meaning.Comment: latex 2e, 11pt, 44 pages; accepted to IJGMMP (2008) as a short
variant of arXiv:0707.1524v3, on 86 page
Integrable matrix equations related to pairs of compatible associative algebras
We study associative multiplications in semi-simple associative algebras over
C compatible with the usual one. An interesting class of such multiplications
is related to the affine Dynkin diagrams of A, D, E-type. In this paper we
investigate in details the multiplications of the A-type and integrable matrix
ODEs and PDEs generated by them.Comment: 12 pages, Late
Brane Gravitational Extension of Dirac's "Extensible Model of the Electron"
A gravitational extension of Dirac's "Extensible model of the electron" is
presented. The Dirac bubble, treated as a 3-dim electrically charged brane, is
dynamically embedded within a 4-dim -symmetric Reissner-Nordstrom bulk.
Crucial to our analysis is the gravitational extension of Dirac's brane
variation prescription; its major effect is to induce a novel geometrically
originated contribution to the energy-momentum tensor on the brane. In turn,
the effective potential which governs the evolution of the bubble exhibits a
global minimum, such that the size of the bubble stays finite (Planck scale)
even at the limit where the mass approaches zero. This way, without
fine-tuning, one avoids the problem so-called 'classical radius of the
electron'.Comment: 6 PRD pages, 4 figures; References adde
The Effect of Radiation Pressure on the Equilibrium Points in the Generalised Photogravitational Restricted Three Body Problem
The existence of equilibrium points and the effect of radiation pressure have
been discussed numerically. The problem is generalized by considering bigger
primary as a source of radiation and small primary as an oblate spheroid. We
have also discussed the Poynting-Robertson(P-R) effect which is caused due to
radiation pressure. It is found that the collinear points deviate
from the axis joining the two primaries, while the triangular points
are not symmetrical due to radiation pressure. We have seen that
are linearly unstable while are conditionally stable in the sense of
Lyapunov when P-R effect is not considered. We have found that the effect of
radiation pressure reduces the linear stability zones while P-R effect induces
an instability in the sense of Lyapunov
Scenario of Accelerating Universe from the Phenomenological \Lambda- Models
Dark matter, the major component of the matter content of the Universe,
played a significant role at early stages during structure formation. But at
present the Universe is dark energy dominated as well as accelerating. Here,
the presence of dark energy has been established by including a time-dependent
term in the Einstein's field equations. This model is compatible with
the idea of an accelerating Universe so far as the value of the deceleration
parameter is concerned. Possibility of a change in sign of the deceleration
parameter is also discussed. The impact of considering the speed of light as
variable in the field equations has also been investigated by using a well
known time-dependent model.Comment: Latex, 9 pages, Major change
Introducing Learning Creative Mathematical Activity for Students in Extra Mathematics Teaching
Chaos, decoherence and quantum cosmology
In this topical review we discuss the connections between chaos, decoherence
and quantum cosmology. We understand chaos as classical chaos in systems with a
finite number of degrees of freedom, decoherence as environment induced
decoherence and quantum cosmology as the theory of the Wheeler - DeWitt
equation or else the consistent history formulation thereof, first in mini
super spaces and later through its extension to midi super spaces. The overall
conclusion is that consideration of decoherence is necessary (and probably
sufficient) to sustain an interpretation of quantum cosmology based on the Wave
function of the Universe adopting a Wentzel - Kramers - Brillouin form for
large Universes, but a definitive account of the semiclassical transition in
classically chaotic cosmological models is not available in the literature yet.Comment: 40 page
Movement Timing and Invariance Arise from Several Geometries
Human movements show several prominent features; movement duration is nearly independent of movement size (the isochrony principle), instantaneous speed depends on movement curvature (captured by the 2/3 power law), and complex movements are composed of simpler elements (movement compositionality). No existing theory can successfully account for all of these features, and the nature of the underlying motion primitives is still unknown. Also unknown is how the brain selects movement duration. Here we present a new theory of movement timing based on geometrical invariance. We propose that movement duration and compositionality arise from cooperation among Euclidian, equi-affine and full affine geometries. Each geometry posses a canonical measure of distance along curves, an invariant arc-length parameter. We suggest that for continuous movements, the actual movement duration reflects a particular tensorial mixture of these canonical parameters. Near geometrical singularities, specific combinations are selected to compensate for time expansion or compression in individual parameters. The theory was mathematically formulated using Cartan's moving frame method. Its predictions were tested on three data sets: drawings of elliptical curves, locomotion and drawing trajectories of complex figural forms (cloverleaves, lemniscates and limaçons, with varying ratios between the sizes of the large versus the small loops). Our theory accounted well for the kinematic and temporal features of these movements, in most cases better than the constrained Minimum Jerk model, even when taking into account the number of estimated free parameters. During both drawing and locomotion equi-affine geometry was the most dominant geometry, with affine geometry second most important during drawing; Euclidian geometry was second most important during locomotion. We further discuss the implications of this theory: the origin of the dominance of equi-affine geometry, the possibility that the brain uses different mixtures of these geometries to encode movement duration and speed, and the ontogeny of such representations
- …