arXiv subjects

Sascha Husa

Publications and source records attributed to Sascha Husa.

113 records · Page 7Linked to original sources

arXiv2000

SU(2) Cosmological Solitons

We present a class of numerical solutions to the SU(2) nonlinear $σ$-model coupled to the Einstein equations with cosmological constant $Λ\geq 0$ in spherical symmetry. These solutions are characterized by the presence of a regular static region which includes a center of symmetry. They are parameterized by a dimensionless ``coupling constant'' $β$, the sign of the cosmological constant, and an integer ``excitation number'' $n$. The phenomenology we find is compared to the corresponding solutions found for the Einstein-Yang-Mills (EYM) equations with positive $Λ$ (EYM$Λ$). If we choose $Λ$ positive and fix $n$, we find a family of static spacetimes with a Killing horizon for $0 \leq β< β_{max}$. As a limiting solution for $β= β_{max}$ we find a {\em globally} static spacetime with $Λ=0$, the lowest excitation being the Einstein static universe. To interpret the physical significance of the Killing horizon in the cosmological context, we apply the concept of a trapping horizon as formulated by Hayward. For small values of $β$ an asymptotically de Sitter dynamic region contains the static region within a Killing horizon of cosmological type. For strong coupling the static region contains an ``eternal cosmological black hole''.

gr-qc↗

arXiv1999

The Asymmetric Merger of Black Holes

We study event horizons of non-axisymmetric black holes and show how features found in axisymmetric studies of colliding black holes and of toroidal black holes are non-generic and how new features emerge. Most of the details of black hole formation and black hole merger are known only in the axisymmetric case, in which numerical evolution has successfully produced dynamical space-times. The work that is presented here uses a new approach to construct the geometry of the event horizon, not by locating it in a given spacetime, but by direct construction. In the axisymmetric case, our method produces the familiar pair-of-pants structure found in previous numerical simulations of black hole mergers, as well as event horizons that go through a toroidal epoch as discovered in the collapse of rotating matter. The main purpose of this paper is to show how new - substantially different - features emerge in the non-axisymmetric case. In particular, we show how black holes generically go through a toroidal phase before they become spherical, and how this fits together with the merger of black holes.

gr-qc↗

arXiv1998

Asymptotically Flat Initial Data for Gravitational Wave Spacetimes, Conformal Compactification and Conformal Symmetry

We study the utilization of conformal compactification within the conformal approach to solving the constraints of general relativity for asymptotically flat initial data. After a general discussion of the framework, particular attention is paid to simplifications that arise when restricting to a class of initial data which have a certain $U(1)\times U(1)$ conformal symmetry.

gr-qc↗

arXiv1996

Initial Data for General Relativity Containing a Marginally Outer Trapped Torus

Asymptotically flat, time-symmetric, axially symmetric and conformally flat initial data for vacuum general relativity are studied numerically on $R^3$ with the interior of a standard torus cut out. By the choice of boundary condition the torus is marginally outer trapped, and thus a surface of minimal area. Apart from pure scaling the standard tori are parameterized by a radius $a\in [0,1]$, where $a=0$ corresponds to the limit where the boundary torus degenerates to a circle and $a=1$ to a torus that touches the axis of symmetry. Noting that these tori are the orbits of a $U(1)\times U(1)$ conformal isometry allows for a simple scheme to solve the constraint, involving numerical solution of only ordinary differential equations.The tori are unstable minimal surfaces (i.e. only saddle points of the area functional) and thus can not be apparent horizons, but are always surrounded by an apparent horizon of spherical topology, which is analyzed in the context of the hoop conjecture and isoperimetric inequality for black holes.

gr-qc↗

arXiv1994

Initial Data for General Relativity with Toroidal Conformal Symmetry

A new class of time-symmetric solutions to the initial value constraints of vacuum General Relativity is introduced. These data are globally regular, asymptotically flat (with possibly several asymptotic ends) and in general have no isometries, but a $U(1)\times U(1)$ group of conformal isometries. After decomposing the Lichnerowicz conformal factor in a double Fourier series on the group orbits, the solutions are given in terms of a countable family of uncoupled ODEs on the orbit space.

gr-qc↗