175 research outputs found
Quasi-local mass in the covariant Newtonian space-time
In general relativity, quasi-local energy-momentum expressions have been
constructed from various formulae. However, Newtonian theory of gravity gives a
well known and an unique quasi-local mass expression (surface integration).
Since geometrical formulation of Newtonian gravity has been established in the
covariant Newtonian space-time, it provides a covariant approximation from
relativistic to Newtonian theories. By using this approximation, we calculate
Komar integral, Brown-York quasi-local energy and Dougan-Mason quasi-local mass
in the covariant Newtonian space-time. It turns out that Komar integral
naturally gives the Newtonian quasi-local mass expression, however, further
conditions (spherical symmetry) need to be made for Brown-York and Dougan-Mason
expressions.Comment: Submit to Class. Quantum Gra
Process and Data: Two Sides of the Same Coin
Companies increasingly adopt process management technology which offers promising perspectives for realizing flexible information systems. However, there still exist numerous process scenarios not adequately covered by contemporary information systems. One major reason for this deficiency is the insufficient understanding of the inherent relationships existing between business processes on one side and business data on the other. Consequently, these two perspectives are not well integrated in many existing process management systems. This paper emphasizes the need for both object- and process-awareness in future information systems, and illustrates it along several examples. Especially, the relation between these two fundamental perspectives will be discussed, and the role of business objects and data as drivers for both process modeling and process enactment be emphasized. In general, any business process support should consider object behavior as well as object interactions, and therefore be based on two levels of granularity. In addition, data-driven process execution and integrated user access to
processes and data are needed. Besides giving insights into these fundamental characteristics, an advanced framework supporting them in an integrated manner will be presented and its application to real-world process scenarios be shown. Overall, a holistic and generic framework integrating processes, data, and users will contribute to overcome many of the limitations of existing process management technology
On all possible static spherically symmetric EYM solitons and black holes
We prove local existence and uniqueness of static spherically symmetric
solutions of the Einstein-Yang-Mills equations for any action of the rotation
group (or SU(2)) by automorphisms of a principal bundle over space-time whose
structure group is a compact semisimple Lie group G. These actions are
characterized by a vector in the Cartan subalgebra of g and are called regular
if the vector lies in the interior of a Weyl chamber. In the irregular cases
(the majority for larger gauge groups) the boundary value problem that results
for possible asymptotically flat soliton or black hole solutions is more
complicated than in the previously discussed regular cases. In particular,
there is no longer a gauge choice possible in general so that the Yang-Mills
potential can be given by just real-valued functions. We prove the local
existence of regular solutions near the singularities of the system at the
center, the black hole horizon, and at infinity, establish the parameters that
characterize these local solutions, and discuss the set of possible actions and
the numerical methods necessary to search for global solutions. That some
special global solutions exist is easily derived from the fact that su(2) is a
subalgebra of any compact semisimple Lie algebra. But the set of less trivial
global solutions remains to be explored.Comment: 26 pages, 2 figures, LaTeX, misprints corrected, 1 reference adde
Null Killing Vector Dimensional Reduction and Galilean Geometrodynamics
The solutions of Einstein's equations admitting one non-null Killing vector
field are best studied with the projection formalism of Geroch. When the
Killing vector is lightlike, the projection onto the orbit space still exists
and one expects a covariant theory with degenerate contravariant metric to
appear, its geometry is presented here. Despite the complications of
indecomposable representations of the local Euclidean subgroup, one obtains an
absolute time and a canonical, Galilean and so-called Newtonian, torsionless
connection. The quasi-Maxwell field (Kaluza Klein one-form) that appears in the
dimensional reduction is a non-separable part of this affine connection, in
contrast to the reduction with a non-null Killing vector. One may define the
Kaluza Klein scalar (dilaton) together with the absolute time coordinate after
having imposed one of the equations of motion in order to prevent the emergence
of torsion. We present a detailed analysis of the dimensional reduction using
moving frames, we derive the complete equations of motion and propose an action
whose variation gives rise to all but one of them. Hidden symmetries are shown
to act on the space of solutions.Comment: LATEX, 41 pages, no figure
Topological geon black holes in Einstein-Yang-Mills theory
We construct topological geon quotients of two families of
Einstein-Yang-Mills black holes. For Kuenzle's static, spherically symmetric
SU(n) black holes with n>2, a geon quotient exists but generically requires
promoting charge conjugation into a gauge symmetry. For Kleihaus and Kunz's
static, axially symmetric SU(2) black holes a geon quotient exists without
gauging charge conjugation, and the parity of the gauge field winding number
determines whether the geon gauge bundle is trivial. The geon's gauge bundle
structure is expected to have an imprint in the Hawking-Unruh effect for
quantum fields that couple to the background gauge field.Comment: 27 pages. v3: Presentation expanded. Minor corrections and addition
Axially Symmetric Bianchi I Yang-Mills Cosmology as a Dynamical System
We construct the most general form of axially symmetric SU(2)-Yang-Mills
fields in Bianchi cosmologies. The dynamical evolution of axially symmetric YM
fields in Bianchi I model is compared with the dynamical evolution of the
electromagnetic field in Bianchi I and the fully isotropic YM field in
Friedmann-Robertson-Walker cosmologies. The stochastic properties of axially
symmetric Bianchi I-Einstein-Yang-Mills systems are compared with those of
axially symmetric YM fields in flat space. After numerical computation of
Liapunov exponents in synchronous (cosmological) time, it is shown that the
Bianchi I-EYM system has milder stochastic properties than the corresponding
flat YM system. The Liapunov exponent is non-vanishing in conformal time.Comment: 18 pages, 6 Postscript figures, uses amsmath,amssymb,epsfig,verbatim,
to appear in CQ
Non-Relativistic Spacetimes with Cosmological Constant
Recent data on supernovae favor high values of the cosmological constant.
Spacetimes with a cosmological constant have non-relativistic kinematics quite
different from Galilean kinematics. De Sitter spacetimes, vacuum solutions of
Einstein's equations with a cosmological constant, reduce in the
non-relativistic limit to Newton-Hooke spacetimes, which are non-metric
homogeneous spacetimes with non-vanishing curvature. The whole non-relativistic
kinematics would then be modified, with possible consequences to cosmology, and
in particular to the missing-mass problem.Comment: 15 pages, RevTeX, no figures, major changes in the presentation which
includes a new title and a whole new emphasis, version to appear in Clas.
Quant. Gra
Sequences of globally regular and black hole solutions in SU(4) Einstein-Yang-Mills theory
SU(4) Einstein-Yang-Mills theory possesses sequences of static spherically
symmetric globally regular and black hole solutions. Considering solutions with
a purely magnetic gauge field, based on the 4-dimensional embedding of
in , these solutions are labelled by the node numbers of
the three gauge field functions , and . We classify the various
types of solutions in sequences and determine their limiting solutions. The
limiting solutions of the sequences of neutral solutions carry charge, and the
limiting solutions of the sequences of charged solutions carry higher charge.
For sequences of black hole solutions with node structure and
, several distinct branches of solutions exist up to critical values
of the horizon radius. We determine the critical behaviour for these sequences
of solutions. We also consider SU(4) Einstein-Yang-Mills-dilaton theory and
show that these sequences of solutions are analogous in most respects to the
corresponding SU(4) Einstein-Yang-Mills sequences of solutions.Comment: 40 pages, 5 tables, 19 Postscript figures, use revtex.st
Sequences of Einstein-Yang-Mills-Dilaton Black Holes
Einstein-Yang-Mills-dilaton theory possesses sequences of neutral static
spherically symmetric black hole solutions. The solutions depend on the dilaton
coupling constant and on the horizon. The SU(2) solutions are labelled
by the number of nodes of the single gauge field function, whereas the
SO(3) solutions are labelled by the nodes of both gauge field
functions. The SO(3) solutions form sequences characterized by the node
structure , where is fixed. The sequences of magnetically neutral
solutions tend to magnetically charged limiting solutions. For finite the
SO(3) sequences tend to magnetically charged Einstein-Yang-Mills-dilaton
solutions with nodes and charge . For and the SO(3) sequences tend to Einstein-Maxwell-dilaton solutions with
magnetic charges and , respectively. The latter also
represent the scaled limiting solutions of the SU(2) sequence. The convergence
of the global properties of the black hole solutions, such as mass, dilaton
charge and Hawking temperature, is exponential. The degree of convergence of
the matter and metric functions of the black hole solutions is related to the
relative location of the horizon to the nodes of the corresponding regular
solutions.Comment: 71 pages, Latex2e, 29 ps-figures include
Standard and Generalized Newtonian Gravities as ``Gauge'' Theories of the Extended Galilei Group - I: The Standard Theory
Newton's standard theory of gravitation is reformulated as a {\it gauge}
theory of the {\it extended} Galilei Group. The Action principle is obtained by
matching the {\it gauge} technique and a suitable limiting procedure from the
ADM-De Witt action of general relativity coupled to a relativistic mass-point.Comment: 51 pages , compress, uuencode LaTex fil
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