39 research outputs found
On Nonlinear -Models arizing in (Super-)Gravity
In a previous paper with Gibbons [CMP 120 (1987) 295] we derived a list of
three dimensional symmetric space -model obtained by dimensional
reduction of a class of four dimensional gravity theories with abelian gauge
fields and scalars. Here we give a detailed analysis of their group theoretical
structure leading to an abstract parametrization in terms of `triangular' group
elements. This allows for a uniform treatment of all these models. As an
interesting application we give a simple derivation of a `Quadratic Mass
Formula' for strictly stationary black holes.Comment: 33 pages, 1 tabl
Classification of Static, Spherically Symmetric Solutions of the Einstein-Yang-Mills Theory with Positive Cosmological Constant
We give a complete classification of all static, spherically symmetric
solutions of the SU(2) Einstein-Yang-Mills theory with a positive cosmological
constant. Our classification proceeds in two steps. We first extend solutions
of the radial field equations to their maximal interval of existence. In a
second step we determine the Carter-Penrose diagrams of all 4-dimensional
space-times constructible from such radial pieces. Based on numerical studies
we sketch a complete phase space picture of all solutions with a regular
origin.Comment: 49 pages, 19 figures, submitted to Commun. Math. Phy
Non-Universality of Critical Behaviour in Spherically Symmetric Gravitational Collapse
The aim of the present letter is to explain the `critical behaviour' observed
in numerical studies of spherically symmetric gravitational collaps of a
perfect fluid. A simple expression results for the critical index of
the black hole mass considered as an order parameter. turns out to
vary strongly with the parameter of the assumed equation of state
.Comment: 6
Self-similar solutions of semilinear wave equations with a focusing nonlinearity
We prove that in three space dimensions a nonlinear wave equation
with being an odd integer has a countable
family of regular spherically symmetric self-similar solutions.Comment: 12 pages, 3 figures, minor corrections to match the published versio
Quantization of the Reissner-Nordstr\"{o}m Black Hole
The Reissner--Nordstr\"{o}m family of solutions can be understood to arise
from the spherically symmetric sector of a nonlinear SO(2,1)/SO(1,1) sigma
model coupled to three dimensional Euclidean gravity. In this context a group
theoretical quantization is performed. We identify the observables of the
theory and calculate their spectra.Comment: 8 pages, Late
Bogomol'nyi Equations for Einstein-Yang-Mills-Dilaton theory
A static, spherically symmetric and purely magnetic solution of the
Einstein-Yang-Mills-Dilaton theory, found previously by numerical integration
is shown to obey a system of first order Bogomol'nyi equations. As common for
such equations, there is a tight relation to supersymmetry, in the present case
to the N=4 gauged SU(2)SU(2) supergravity of Freedman and Schwarz.
Specifically, the dilaton potential of the latter can be avoided by choosing
one of the two gauge coupling constants to be imaginary. It is argued that this
corresponds to a hitherto unknown N=4 gauged SU(2)SU(1,1) supergravity
in four Euclidean dimensions leading to Bogomol'nyi equations with
asymptotically flat solutions.Comment: 13 pages, LaTeX, 2 epsf figures, uses elsar
Mass inflation and chaotic behaviour inside hairy black holes
We analyze the interior geometry of static, spherically symmetric black holes
of the Einstein-Yang-Mills-Higgs theory. Generically the solutions exhibit a
behaviour that may be described as ``mass inflation'', although with a
remarkable difference between the cases with and without a Higgs field. Without
Higgs field the YM field induces a kind of cyclic behaviour leading to repeated
cycles of mass inflation - taking the form of violent explosions - interrupted
by quiescent periods and subsequent approaches to an almost Cauchy horizon.
With the Higgs field no such cycles occur. In addition there are non-generic
families with a Schwarzschild resp. Reissner-Nordstr{\o}m type singularity at
r=0.Comment: 22 pages, Latex, 5 figures (8 eps files
A Remark on the Instability of the Bartnik-McKinnon Solutions
The aim of the present letter is to critically review the stability of the
Bartnik-McKinnon solutions of the Einstein-Yang-Mills theory. The stability
question was already studied by several authors, but there seems to be some
confusion about the nature and the number of unstable modes. We suggest to
distinguish two different kind of instabilities, which we call `gravitational'
respectively `sphaleron' instabilities. We claim that the
Bartnik-McKinnon solution has exactly unstable modes, of either type.Comment: LaTex, 6 p., MPI-PhT/94-6
Rotating Einstein-Maxwell-Dilaton Black Holes in D Dimensions
We construct exact charged rotating black holes in Einstein-Maxwell-dilaton
theory in spacetime dimensions, , by embedding the dimensional
Myers-Perry solutions in dimensions, and performing a boost with a
subsequent Kaluza-Klein reduction. Like the Myers-Perry solutions, these black
holes generically possess independent angular momenta. We present
the global and horizon properties of these black holes, and discuss their
domains of existence.Comment: 12 pages, 6 figue