1,376 research outputs found
Investigation of the Interior of Colored Black Holes and the Extendability of Solutions of the Einstein-Yang/Mills Equations
We prove that any asymptotically flat solution to the spherically symmetric
SU(2) Einstein-Yang/Mills equations is globally defined. This result applies in
particular to the interior of colored black holes.Comment: Latex, 8 gif figure
Reissner-Nordstrom-like solutions of the SU(2) Einstein-Yang/Mills (EYM) equations
In this paper we study a new type of solution of the spherically symmetric,
Einstein-Yang/Mills (EYM) equations with SU(2) gauge group. These solutions are
well-behaved in the far-field, and have a Reissner-Nordstrom type essential
singularity at the origin. These solutions display some novel features which
are not present in particle-like, or black-hole solutions. Any spherically
symmetric solution to the EYM equations, defined in the far-field, is either a
particle-like solution, a black-hole solution, or one of these RNL solutions.Comment: 5 pages, latex, no figures, Submitted to Comm. Math. Phys. January
15, 199
Hairy Black Holes, Horizon Mass and Solitons
Properties of the horizon mass of hairy black holes are discussed with
emphasis on certain subtle and initially unexpected features. A key property
suggests that hairy black holes may be regarded as `bound states' of ordinary
black holes without hair and colored solitons. This model is then used to
predict the qualitative behavior of the horizon properties of hairy black
holes, to provide a physical `explanation' of their instability and to put
qualitative constraints on the end point configurations that result from this
instability. The available numerical calculations support these predictions.
Furthermore, the physical arguments are robust and should be applicable also in
more complicated situations where detailed numerical work is yet to be carried
out.Comment: 25 pages, 5 (new) figures. Revtex file. Final version to appear in
CQ
Cosmological Analogues of the Bartnik--McKinnon Solutions
We present a numerical classification of the spherically symmetric, static
solutions to the Einstein--Yang--Mills equations with cosmological constant
. We find three qualitatively different classes of configurations,
where the solutions in each class are characterized by the value of
and the number of nodes, , of the Yang--Mills amplitude. For sufficiently
small, positive values of the cosmological constant, \Lambda < \Llow(n), the
solutions generalize the Bartnik--McKinnon solitons, which are now surrounded
by a cosmological horizon and approach the deSitter geometry in the asymptotic
region. For a discrete set of values , the solutions are topologically --spheres, the ground state
being the Einstein Universe. In the intermediate region, that is for
\Llow(n) < \Lambda < \Lhig(n), there exists a discrete family of global
solutions with horizon and ``finite size''.Comment: 16 pages, LaTeX, 9 Postscript figures, uses epsf.st
On the monotonicity of the time-map
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/28073/1/0000517.pd
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
Multiply Warped Products with Non-Smooth Metrics
In this article we study manifolds with -metrics and properties of
Lorentzian multiply warped products. We represent the interior Schwarzschild
space-time as a multiply warped product space-time with warping functions and
we also investigate the curvature of a multiply warped product with
-warping functions. We given the {\it{Ricci curvature}} in terms of ,
for the multiply warped products of the form $M=(0,\
2m)\times_{f_1}R^1\times_{f_2} S^2$.Comment: LaTeX, 7 page
Generic bifurcation of steady-state solutions
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/24837/1/0000263.pd
Symmetry-breaking under small perturbations
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46160/1/205_2005_Article_BF01055753.pd
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
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