211 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
Functions of linear operators: Parameter differentiation
We derive a useful expression for the matrix elements of the derivative of a function of a
diagonalizable linear operator with respect to the parameter . The
function is supposed to be an operator acting on the same space as
the operator . We use the basis which diagonalizes A(t), i.e., , and obtain . In addition to this, we show that
further elaboration on the (not necessarily simple) integral expressions given
by Wilcox 1967 (who basically considered of the exponential type) and
generalized by Rajagopal 1998 (who extended Wilcox results by considering
of the -exponential type where with ; hence,
yields this same expression. Some of the lemmas first established by the above
authors are easily recovered.Comment: No figure
Measurement in biological systems from the self-organisation point of view
Measurement in biological systems became a subject of concern as a
consequence of numerous reports on limited reproducibility of experimental
results. To reveal origins of this inconsistency, we have examined general
features of biological systems as dynamical systems far from not only their
chemical equilibrium, but, in most cases, also of their Lyapunov stable states.
Thus, in biological experiments, we do not observe states, but distinct
trajectories followed by the examined organism. If one of the possible
sequences is selected, a minute sub-section of the whole problem is obtained,
sometimes in a seemingly highly reproducible manner. But the state of the
organism is known only if a complete set of possible trajectories is known. And
this is often practically impossible. Therefore, we propose a different
framework for reporting and analysis of biological experiments, respecting the
view of non-linear mathematics. This view should be used to avoid
overoptimistic results, which have to be consequently retracted or largely
complemented. An increase of specification of experimental procedures is the
way for better understanding of the scope of paths, which the biological system
may be evolving. And it is hidden in the evolution of experimental protocols.Comment: 13 pages, 5 figure
Late Time Tail of Wave Propagation on Curved Spacetime
The late time behavior of waves propagating on a general curved spacetime is
studied. The late time tail is not necessarily an inverse power of time. Our
work extends, places in context, and provides understanding for the known
results for the Schwarzschild spacetime. Analytic and numerical results are in
excellent agreement.Comment: 11 pages, WUGRAV-94-1
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
Plasmarings as dual black rings
We construct solutions to the relativistic Navier-Stokes equations that
describe the long wavelength collective dynamics of the deconfined plasma phase
of N=4 Yang Mills theory compactified down to d=3 on a Scherk-Schwarz circle
and higher dimensional generalisations. Our solutions are stationary, axially
symmetric spinning balls and rings of plasma. These solutions, which are dual
to (yet to be constructed) rotating black holes and black rings in
Scherk-Schwarz compactified AdS(5) and AdS(6), and have properties that are
qualitatively similar to those of black holes and black rings in flat five
dimensional supergravity.Comment: 40 pages, 40 figures. (v2) Correction to black brane equation of
state, additional reference
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
Linear Stability of Triangular Equilibrium Points in the Generalized Photogravitational Restricted Three Body Problem with Poynting-Robertson Drag
In this paper we have examined the linear stability of triangular equilibrium
points in the generalised photogravitational restricted three body problem with
Poynting-Robertson drag. We have found the position of triangular equilibrium
points of our problem. The problem is generalised in the sense that smaller
primary is supposed to be an oblate spheroid. The bigger primary is considered
as radiating. The equations of motion are affected by radiation pressure force,
oblateness and P-R drag. All classical results involving photogravitational and
oblateness in restricted three body problem may be verified from this result.
With the help of characteristic equation, we discussed the stability. Finally
we conclude that triangular equilibrium points are unstable.Comment: accepted for publication in Journal of Dynamical Systems & Geometric
Theories Vol. 4, Number 1 (2006
Pictorial Representation for Antisymmetric Eigenfunctions of PS-3 Integral Equations
Eigenvalue problem for Poincare-Steklov-3 integral equation is reduced to the
solution of three transcendential equations for three unknown numbers, moduli
of pants. The complete list of antisymmetric eigenfunctions of integral
equation in terms of Kleinian membranes is given.Comment: 33 pages, 13 figures. This paper is an extended version of CV/061173
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
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