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

AdS5_5 rotating non-Abelian black holes

We present arguments for the existence of charged, rotating black holes with equal magnitude angular momenta in $d=5$ 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 $d$ odd. The metric used possesses $(d+1)/2$ Killing vectors and the solutions have $(d-1)/2$ 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