Peter C. Aichelburg

On the Gravitational field of a massless particle

The gravitational field of a massless point particle is first calculated using the linearized field equations. The result is identical with the exact solution, obtained from the Schwarzschild metric by means of a singular Lorentz transformation. The gravitational field of the particle is nonvanishing only on a plane containing the particle and orthogonal to the direction of motion. On this plane the Riemann tensor has a δ-like singularity and is exactly of Petrov typeN.

Magnetically charged black holes and their stability

We study magnetically charged black holes in the Einstein-Yang-Mills-Higgs theory in the limit of infinitely strong coupling of the Higgs field. Using mixed analytical and numerical methods we give a complete description of static spherically symmetric black hole solutions, both Abelian and non-Abelian. In particular, we find a new class of extremal non-Abelian solutions. We show that all non-Abelian solutions are stable against linear radial perturbations. The implications of our results for the semiclassical evolution of magnetically charged black holes are discussed.

Generalized symmetries of impulsive gravitational waves

We generalize previous \cite{AiBa2} work on the classification of (

Necessary and sufficient conditions for trivial solutions in supergravity

C^\infty

News from critical collapse: Bondi mass, tails, and quasinormal modes

) symmetries of plane-fronted waves with an impulsive profile. Due to the specific form of the profile it is possible to extend the group of normal-form-preserving diffeomorphisms to include non-smooth transformations. This extension entails a richer structure of the symmetry algebra generated by the (non-smooth) Killing vectors.We generalize previous work on the classification of (C∞) symmetries of plane-fronted waves with an impulsive profile. Due to the specific form of the profile it is possible to extend the group of normal-form-preserving diffeomorphisms to include non-smooth transformations. This extension entails a richer structure of the symmetry algebra generated by the (non-smooth) Killing vectors.

Type II Critical Collapse of a Self-Gravitating Nonlinear Sigma Model

We determine the conditions necessary for a solution of the supergravity field equations with infinitesimal spin-3/2 field to be a pure gauge transformation of an Einstein vacuum field. The analysis depends on the Petrov classification of the curvature tensor and uses two-component spinor calculus. For general type I, the type II, and typeD, the necessary conditions found are also shown to be sufficient, and the explicit form of the gauge transformation can be given.

Identification of trivial solutions in supergravity

We discuss critical gravitational collapse on the threshold of apparent horizon formation as a model both for the discussion of global aspects of critical collapse and for numerical studies in a compactified context. For our matter model we choose a self-gravitating massless scalar field in spherical symmetry, which has been studied extensively in the critical collapse literature. Our evolution system is based on Bondi coordinates, the mass-function is used as an evolution variable to ensure regularity at null infinity. We compute radiation quantities like the Bondi mass and news-function and find that they reflect the discretely self-similar (DSS) behavior. Surprisingly, the period of radiation at null infinity is related to the formal result for the leading quasinormal mode of a black hole with rapidly decreasing mass. Furthermore, our investigations shed some light on global versus local issues in critical collapse, and the validity and usefulness of the concept of null infinity when predicting detector signals.

Tails for the Einstein–Yang–Mills system

We report on the existence and phenomenology of type II critical collapse within the one-parameter family of SU(2) σ models coupled to gravity. Numerical investigations in spherical symmetry show discretely self-similar (DSS) behavior at the threshold of black hole formation for values of the dimensionless coupling constant η ranging from 0.2 to 100; at 0.18 we see small deviations from DSS. While the echoing period Δ of the critical solution rises sharply towards the lower limit of this range, the characteristic mass scaling has a critical exponent γ which is almost independent of η, asymptoting to 0.1185±0.0005 at large η. We also find critical scaling of the scalar curvature for near-critical initial data. Our numerical results are based on an outgoing–null-cone formulation of the Einstein-matter equations, specialized to spherical symmetry. Our numerically computed initial-data critical parameters show second order convergence with the grid resolution, and after compensating for this variation in our individual evolutions are uniformly second order convergent even very close to criticality.

On the mode stability of a self-similar wave map

Abstract The problem of when a given solution to the supergravity field equations can be transformed to an Einstein vacuum solution by a supersymmetry gauge transformation is considered. It is shown that the conditions that infinitesimally gauge-related solutions are required to fulfill depend on the algebraic structure of the Riemann tensor. For general Petrov type I, type II and type D, these conditions are not only necessary but also sufficient .

SU(2) Cosmological Solitons

We study numerically the late-time behaviour of the coupled Einstein–Yang–Mills system. We restrict ourselves to spherical symmetry and employ Bondi-like coordinates with radial compactification. Numerical results exhibit tails with exponents close to −4 at timelike infinity i+ and −2 at future null infinity .