167 research outputs found
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
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
A rigorous formulation of the cosmological Newtonian limit without averaging
We prove the existence of a large class of one-parameter families of
cosmological solutions to the Einstein-Euler equations that have a Newtonian
limit. This class includes solutions that represent a finite, but otherwise
arbitrary, number of compact fluid bodies. These solutions provide exact
cosmological models that admit Newtonian limits but, are not, either implicitly
or explicitly, averaged
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
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
Connections and dynamical trajectories in generalised Newton-Cartan gravity I. An intrinsic view
The "metric" structure of nonrelativistic spacetimes consists of a one-form
(the absolute clock) whose kernel is endowed with a positive-definite metric.
Contrarily to the relativistic case, the metric structure and the torsion do
not determine a unique Galilean (i.e. compatible) connection. This subtlety is
intimately related to the fact that the timelike part of the torsion is
proportional to the exterior derivative of the absolute clock. When the latter
is not closed, torsionfreeness and metric-compatibility are thus mutually
exclusive. We will explore generalisations of Galilean connections along the
two corresponding alternative roads in a series of papers. In the present one,
we focus on compatible connections and investigate the equivalence problem
(i.e. the search for the necessary data allowing to uniquely determine
connections) in the torsionfree and torsional cases. More precisely, we
characterise the affine structure of the spaces of such connections and display
the associated model vector spaces. In contrast with the relativistic case, the
metric structure does not single out a privileged origin for the space of
metric-compatible connections. In our construction, the role of the Levi-Civita
connection is played by a whole class of privileged origins, the so-called
torsional Newton-Cartan (TNC) geometries recently investigated in the
literature. Finally, we discuss a generalisation of Newtonian connections to
the torsional case.Comment: 79 pages, 7 figures; v2: added material on affine structure of
connection space, former Section 4 postponed to 3rd paper of the serie
Global behavior of solutions to the static spherically symmetric EYM equations
The set of all possible spherically symmetric magnetic static
Einstein-Yang-Mills field equations for an arbitrary compact semi-simple gauge
group was classified in two previous papers. Local analytic solutions near
the center and a black hole horizon as well as those that are analytic and
bounded near infinity were shown to exist. Some globally bounded solutions are
also known to exist because they can be obtained by embedding solutions for the
case which is well understood. Here we derive some asymptotic
properties of an arbitrary global solution, namely one that exists locally near
a radial value , has positive mass at and develops no
horizon for all . The set of asymptotic values of the Yang-Mills
potential (in a suitable well defined gauge) is shown to be finite in the
so-called regular case, but may form a more complicated real variety for models
obtained from irregular rotation group actions.Comment: 43 page
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
Post-Newtonian extension of the Newton-Cartan theory
The theory obtained as a singular limit of General Relativity, if the
reciprocal velocity of light is assumed to tend to zero, is known to be not
exactly the Newton-Cartan theory, but a slight extension of this theory. It
involves not only a Coriolis force field, which is natural in this theory
(although not original Newtonian), but also a scalar field which governs the
relation between Newtons time and relativistic proper time. Both fields are or
can be reduced to harmonic functions, and must therefore be constants, if
suitable global conditions are imposed. We assume this reduction of
Newton-Cartan to Newton`s original theory as starting point and ask for a
consistent post-Newtonian extension and for possible differences to usual
post-Minkowskian approximation methods, as developed, for example, by
Chandrasekhar. It is shown, that both post-Newtonian frameworks are formally
equivalent, as far as the field equations and the equations of motion for a
hydrodynamical fluid are concerned.Comment: 13 pages, LaTex, to appear in Class. Quantum Gra
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
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