Betti Hartmann

Holographic Superconductors in 3+1 dimensions away from the probe limit

We study holographic superconductors in 3+1 dimensions away from the probe limit, i.e. taking backreaction of the space-time into account. We consider the case of pure Einstein and Gauss-Bonnet gravity, respectively. Similar to the probe limit we observe that the critical temperature at which condensation sets in decreases with increasing Gauss-Bonnet coupling. The decrease is however stronger when taking backreaction of the space-time into account. We observe that the critical temperature becomes very small, but stays positive for all values of the Gauss-Bonnet coupling no matter how strong the backreaction of the space-time is.

Electrons on hexagonal lattices and applications to nanotubes

We consider a Frohlich-type Hamiltonian on a hexagonal lattice. Aiming to describe nanotubes, we choose this two-dimensional lattice to be periodic and to have a large extension in one (x) direction and a small extension in the other (y) direction. We study the existence of solitons in this model using both analytical and numerical methods. We find exact solutions of our equations and discuss some of their properties.

Holographic superfluid/fluid/insulator phase transitions in 2+1 dimensions

We study the breaking of an Abelian symmetry close to the horizon of a black string as well as close to the tip of a solitonic, cigar-shaped solution in (3+1)-dimensional Anti-de Sitter space-time. We use these solutions to describe holographic superfluids away from the probe limit, i.e. taking backreaction into account. We observe that up to four phases exist in this model representing the duals of black string solutions with and without scalar hair and solitonic, cigar-shaped solutions with and without scalar hair, respectively. We construct the full phase diagram that describes the phase transitions between fluids and superfluids, between insulators and superfluids as well as between insulators and fluids. In the probe limit the phase transition from fluids to black string superfluids changes from being second order to first order for sufficiently large values of the superfluid velocity and/or the angular momentum of the dual black string. We find that if we take backreaction into account phase transitions that are first order for weak backreaction become again second order for sufficiently strong backreaction. Moreover, we find a new type of insulator/superfluid phase transition for strong backreaction and vanishing superfluid velocity as well as a new type of fluid/superfluid phase transition that exists only for non-vanishing superfluid velocity.

Rotating boson stars in five dimensions

We study rotating boson stars in five spacetime dimensions. The boson fields consist of a complex doublet scalar field. Considering boson stars rotating in two orthogonal planes with both angular momenta of equal magnitude, a special ansatz for the boson field and the metric allows for solutions with nontrivial dependence on the radial coordinate only. The charge of the scalar field equals the sum of the angular momenta. The rotating boson stars are globally regular and asymptotically flat. For our choice of a sextic potential, the rotating boson star solutions possess a flat spacetime limit. We study the solutions in flat and curved spacetime.

Gravitationally bound monopoles.

We construct monopole solutions in SU(2) Einstein-Yang-Mills-Higgs theory carrying magnetic charge n. For vanishing and small Higgs self-coupling, these multimonopole solutions are gravitationally bound. Their mass per unit charge is lower than the mass of the n = 1 monopole. For large Higgs self-coupling only a repulsive phase exists.

Higher order curvature generalizations of Bartnick-McKinnon and coloured black hole solutions in d = 5

Abstract We construct globally regular as well as non-Abelian black hole solutions of a higher-order curvature Einstein–Yang–Mills (EYM) model in d =5 dimensions. This model consists of the superposition of the first two members of the gravitational hierarchy (Einstein plus first Gauss–Bonnet (GB)) interacting with the superposition of the first two members of the SO ( d ) Yang–Mills hierarchy.

GRAVITATING DYONS AND DYONIC BLACK HOLES

We study static spherically symmetric gravitating dyon solutions and dyonic black holes in Einstein-Yang-Mills-Higgs theory. The gravitating dyon solutions share many features with the gravitating monopole solutions. In particular, gravitating dyon solutions and dyonic black holes exist only up to a maximal coupling constant, and beside the fundamental dyon solutions there are excited dyon solutions.

The Complete set of solutions of the geodesic equations in the space-time of a Schwarzschild black hole pierced by a cosmic string

We study the geodesic equation in the space-time of a Schwarzschild black hole pierced by an infinitely thin cosmic string and give the complete set of analytical solutions of this equation for massive and massless particles, respectively. The solutions of the geodesic equations can be classified according to the particles energy and angular momentum, the ratio between the component of the angular momentum aligned with the axis of the string and the total angular momentum, the deficit angle of the space-time and as well the horizon radius (or mass) of the black hole. For bound orbits of massive test particles we calculate the perihelion shift, we discuss light deflection and comment on the Newtonian limit.

Test particle motion in the space-time of a Kerr black hole pierced by a cosmic string

We study the geodesic equation in the space-time of a Kerr black hole pierced by an infinitely thin cosmic string and give the complete set of analytical solutions of this equation for massive and massless particles in terms of Mino time that allows one to decouple the r and {theta} components of the geodesic equation. The solutions of the geodesic equation can be classified according to the particles energy and angular momentum, the mass and angular momentum per mass of the black hole. We give examples of orbits showing the influence of the cosmic string. We also discuss the perihelion shift and the Lense-Thirring effect for bound orbits and show that the presence of a cosmic string enhances both effects. Comparing our results with experimental data from the LAGEOS satellites we find an upper bound on the energy per unit length of a string piercing the earth which is approximately 10{sup 16} kg/m. Our work has also applications to the recently suggested explanation of the alignment of the polarization vector of quasars using remnants of cosmic string decay in the form of primordial magnetic field loops.

Dyons with axial symmetry

We construct axially symmetric dyons in SU(2) Yang–Mills–Higgs theory. In the Prasad–Sommerfield limit, they are obtained via scaling relations from axially symmetric multimonopole solutions. For finite Higgs self-coupling they are constructed numerically.