460 research outputs found
Rotating Boson Stars and Q-Balls
We consider axially symmetric, rotating boson stars. Their flat space limits
represent spinning Q-balls. We discuss their properties and determine their
domain of existence. Q-balls and boson stars are stationary solutions and exist
only in a limited frequency range. The coupling to gravity gives rise to a
spiral-like frequency dependence of the boson stars. We address the flat space
limit and the limit of strong gravitational coupling. For comparison we also
determine the properties of spherically symmetric Q-balls and boson stars.Comment: 22 pages, 18 figure
AdS rotating non-Abelian black holes
We present arguments for the existence of charged, rotating black holes with
equal magnitude angular momenta in Einstein-Yang-Mills theory with
negative cosmological constant. These solutions posses a regular horizon of
spherical topology and approach asymptotically the Anti-de Sitter spacetime
background. The black hole solutions have also an electric charge and a
nonvanishing magnetic flux through the sphere at infinity. Different from the
static case, no regular solution with a nonvanishing angular momenta is found
for a vanishing event horizon radius.Comment: 14 pages, 7 figure
Black strings in (4+1)-dimensional Einstein-Yang-Mills theory
We study two classes of static uniform black string solutions in a
(4+1)-dimensional SU(2) Einstein-Yang-Mills model. These configurations possess
a regular event horizon and corresponds in a 4-dimensional picture to axially
symmetric black hole solutions in an Einstein-Yang-Mills-Higgs-U(1)-dilaton
theory. In this approach, one set of solutions possesses a nonzero magnetic
charge, while the other solutions represent black holes located in between a
monopole-antimonopole pair. A detailed analysis of the solutions' properties is
presented, the domain of existence of the black strings being determined. New
four dimensional solutions are found by boosting the five dimensional
configurations. We also present an argument for the non-existence of finite
mass hyperspherically symmetric black holes in SU(2) Einstein-Yang-Mills
theory.Comment: 19 Revtex pages, 27 eps-figures; discussion on rotating black holes
modifie
Modeling planar degenerate wetting and anchoring in nematic liquid crystals
We propose a simple surface potential favoring the planar degenerate
anchoring of nematic liquid crystals, i.e., the tendency of the molecules to
align parallel to one another along any direction parallel to the surface. We
show that, at lowest order in the tensorial Landau-de Gennes order-parameter,
fourth-order terms must be included. We analyze the anchoring and wetting
properties of this surface potential. In the nematic phase, we find the desired
degenerate planar anchoring, with positive scalar order-parameter and some
surface biaxiality. In the isotropic phase, we find, in agreement with
experiments, that the wetting layer may exhibit a uniaxial ordering with
negative scalar order-parameter. For large enough anchoring strength, this
negative ordering transits towards the planar degenerate state
Fast iterative solution of reaction-diffusion control problems arising from chemical processes
PDE-constrained optimization problems, and the development of preconditioned iterative methods for the efficient solution of the arising matrix system, is a field of numerical analysis that has recently been attracting much attention. In this paper, we analyze and develop preconditioners for matrix systems that arise from the optimal control of reaction-diffusion equations, which themselves result from chemical processes. Important aspects in our solvers are saddle point theory, mass matrix representation and effective Schur complement approximation, as well as the outer (Newton) iteration to take account of the nonlinearity of the underlying PDEs
Regularization-robust preconditioners for time-dependent PDE constrained optimization problems
In this article, we motivate, derive and test �effective preconditioners to be used with the Minres algorithm for solving a number of saddle point systems, which arise in PDE constrained optimization problems. We consider the distributed control problem involving the heat equation with two diff�erent functionals, and the Neumann boundary control problem involving Poisson's equation and the heat equation. Crucial to the eff�ectiveness of our preconditioners in each case is an eff�ective approximation of the Schur complement of the matrix system. In each case, we state the problem being solved, propose the preconditioning approach, prove relevant eigenvalue bounds, and provide numerical results which demonstrate that our solvers are eff�ective for a wide range of regularization parameter values, as well as mesh sizes and time-steps
Spherically symmetric Yang-Mills solutions in a (4+n)- dimensional space-time
We consider the Einstein-Yang-Mills Lagrangian in a (4+n)-dimensional
space-time. Assuming the matter and metric fields to be independent of the n
extra coordinates, a spherical symmetric Ansatz for the fields leads to a set
of coupled ordinary differential equations. We find that for n > 1 only
solutions with either one non-zero Higgs field or with all Higgs fields
constant exist. We construct the analytic solutions which fulfill this
conditions for arbitrary n, namely the Einstein-Maxwell-dilaton solutions. We
also present generic solutions of the effective 4-dimensional
Einstein-Yang-Mills-Higgs-dilaton model, which possesses n Higgs triplets
coupled in a specific way to n independent dilaton fields. These solutions are
the abelian Einstein-Maxwell- dilaton solutions and analytic non-abelian
solutions, which have diverging Higgs fields. In addition, we construct
numerically asymptotically flat and finite energy solutions for n=2.Comment: 15 Latex pages, 4 eps figures; v2: discussion of results revisite
Charged-Rotating Black Holes in Higher-dimensional (A)DS-Gravity
We present numerical evidences for the existence of rotating black hole
solutions in d-dimensional Einstein-Maxwell theory with a cosmological constant
and for odd. The metric used possesses Killing vectors and the
solutions have equal angular momenta. A Schwarschild-type coordinate
is used for the radial variable and both signs of the cosmological constant are
emphasized. Several properties of the solutions are studied, namely their
surface gravity, mass and angular momentum as functions of two parameters: the
magnetic field and the angular velocity at the horizon. The influence of the
electromagnetic field on the domain of existence of the black holes is studied
are compared to the vacuum case where analytic solutions are available.Comment: 20 pages, 12 figures, results extended, references adde
Orbits in the Field of a Gravitating Magnetic Monopole
Orbits of test particles and light rays are an important tool to study the
properties of space-time metrics. Here we systematically study the properties
of the gravitational field of a globally regular magnetic monopole in terms of
the geodesics of test particles and light. The gravitational field depends on
two dimensionless parameters, defined as ratios of the characteristic mass
scales present. For critical values of these parameters the resulting metric
coefficients develop a singular behavior, which has profound influence on the
properties of the resulting space-time and which is clearly reflected in the
orbits of the test particles and light rays.Comment: 24 pages, 15 figures. Accepted for publication in GR
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