84 research outputs found
A generalization of the Lieb-Thirring inequalities in low dimensions
We give an estimate for the moments of the negative eigenvalues of elliptic operators on ]Rn in low dimensions. The estimate is a generalization of the Lieb-Thirring inequalities in one or two dimensions. We use the cp-transform decomposition of Frazier and J awerth
Dynamics of Gravitating Magnetic Monopoles
According to previous work on magnetic monopoles, static regular solutions
are nonexistent if the vacuum expectation value of the Higgs field is
larger than a critical value , which is of the order of the
Planck mass. In order to understand the properties of monopoles for
, we investigate their dynamics numerically. If is
large enough (), a monopole expands exponentially and a
wormhole structure appears around it, regardless of coupling constants and
initial configuration. If is around , there are three
types of solutions, depending on coupling constants and initial configuration:
a monopole either expands as stated above, collapses into a black hole, or
comes to take a stable configuration.Comment: 11 pages, revtex, postscript figures; results for various initial
conditions are added; to appear in Phys. Rev.
Gravitational Properties of Monopole Spacetimes Near the Black Hole Threshold
Although nonsingular spacetimes and those containing black holes are
qualitatively quite different, there are continuous families of configurations
that connect the two. In this paper we use self-gravitating monopole solutions
as tools for investigating the transition between these two types of
spacetimes. We show how causally distinct regions emerge as the black hole
limit is achieved, even though the measurements made by an external observer
vary continuously. We find that near-critical solutions have a naturally
defined entropy, despite the absence of a true horizon, and that this has a
clear connection with the Hawking-Bekenstein entropy. We find that certain
classes of near-critical solutions display naked black hole behavior, although
they are not truly black holes at all. Finally, we present a numerical
simulation illustrating how an incident pulse of matter can induce the
dynamical collapse of a monopole into an extremal black hole. We discuss the
implications of this process for the third law of black hole thermodynamics.Comment: 23 pages, 4 figures RevTe
Cosmic Colored Black Holes
We present spherically symmetric static solutions (a particle-like solution
and a black hole solution) in the Einstein-Yang-Mills system with a
cosmological constant.Although their gravitational structures are locally
similar to those of the Bartnik-McKinnon particles or the colored black holes,
the asymptotic behavior becomes quite different because of the existence of a
cosmological horizon. We also discuss their stability by means of a catastrophe
theory as well as a linear perturbation analysis and find the number of
unstable modes.Comment: 12 pages, latex, 4 figures (available upon request
Gravitating dyons and dyonic black holes in Einstein-Born-Infeld-Higgs model
We find static spherically symmetric dyons in Einstein-Born-Infeld-Higgs
model in 3+1 dimensions. The solutions share many features with the gravitating
monopoles in the same model. In particular, they exist only up to some critical
value of a parameter \a related to the strength of the gravitational
interaction. We also study dyonic non-Abelian black holes. We analyse these
solutions numerically.Comment: Minor modifications, few more references added. To appear in Phys.
Lett.
Internal structure of Skyrme black hole
We consider the internal structure of the Skyrme black hole under a static
and spherically symmetric ansatz. $@u8(Be concentrate on solutions with the
node number one and with the "winding" number zero, where there exist two
solutions for each horizon radius; one solution is stable and the other is
unstable against linear perturbation. We find that a generic solution exhibits
an oscillating behavior near the sigularity, as similar to a solution in the
Einstein-Yang-Mills (EYM) system, independently to stability of the solution.
Comparing it with that in the EYM system, this oscillation becomes mild because
of the mass term of the Skyrme field. We also find Schwarzschild-like
exceptional solutions where no oscillating behavior is seen. Contrary to the
EYM system where there is one such solution branch if the node number is fixed,
there are two branches corresponding to the stable and the unstable ones.Comment: 5 pages, 4 figures, some contents adde
Polar Perturbations of Self-gravitating Supermassive Global Monopoles
Spontaneous global symmetry breaking of O(3) scalar field gives rise to
point-like topological defects, global monopoles. By taking into account
self-gravity,the qualitative feature of the global monopole solutions depends
on the vacuum expectation value v of the scalar field. When v < sqrt{1 / 8 pi},
there are global monopole solutions which have a deficit solid angle defined at
infinity. When sqrt{1 / 8 pi} <= v < sqrt{3 / 8 pi}, there are global monopole
solutions with the cosmological horizon, which we call the supermassive global
monopole. When v >= sqrt{3 / 8 pi}, there is no nontrivial solution. It was
shown that all of these solutions are stable against the spherical
perturbations. In addition to the global monopole solutions, the de Sitter
solutions exist for any value of v. They are stable against the spherical
perturbations when v sqrt{3 / 8 pi}.
We study polar perturbations of these solutions and find that all
self-gravitating global monopoles are stable even against polar perturbations,
independently of the existence of the cosmological horizon, while the de Sitter
solutions are always unstable.Comment: 10 pages, 6 figures, corrected some type mistakes (already corrected
in PRD version
- âŠ