Herbert Balasin

Geodesics for impulsive gravitational waves and the multiplication of distributions

We consider particle trajectories in the gravitational field of an impulsive pp-wave. Due to the distributional character of the wave profiles, one inevitably encounters an ambiguous point value . We show that this ambiguity may be resolved by imposing covariant constancy of the square of the tangent. Our result is consistent with Colombeaus multiplication of distributions.We consider particle trajectories in the gravitational field of an impulsive pp-wave. Due to the distributional character of the wave profile one inevitably encounters an ambiguous point value

Distributional energy--momentum tensor of the Kerr--Newman spacetime family

\theta(0)

The energy-momentum tensor of a black hole, or what curves the Schwarzschild geometry?

. We show that this ambiguity may be resolved by imposing covariant constancy of the square of the tangent. Our result is consistent with Colombeaus multiplication of distributions.

The ultrarelativistic Kerr geometry and its energy-momentum tensor

Using the Kerr--Schild decomposition of the metric tensor that employs the algebraically special nature of the Kerr--Newman spacetime family, we calculate the energy--momentum tensor. The latter turns out to be a well defined tensor distribution with disc-like support.

Generalized symmetries of impulsive gravitational waves

Using distributional techniques we calculate the energy-momentum tensor of the Schwarzschild geometry. It turns out to be a well defined tensor distribution concentrated on the r=0 region which is usually excluded from spacetime. This provides a physical interpretation for the curvature of this geometry.

Boosting the Kerr geometry in an arbitrary direction

The ultrarelativistic limit of the Schwarzschild and Kerr geometries, together with their respective energy-momentum tensors, is derived. Our approach is based on tensor distributions making use of the underlying Kerr-Schild structure, which remains stable under the ultrarelativistic boost.

Wong's Equations and Charged Relativistic Particles in Non-Commutative Space

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

The spherically symmetric Standard Model with gravity

C^\infty

The ultrarelativistic limit of 2D dilaton gravity and its energy?momentum tensor

) 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.

On the energy-momentum tensor in Moyal space

We construct ultrarelativistic Kerr geometries from their distributional energy - momentum tensors. The latter are obtained by boosting Kerrs distributional energy - momentum tensor in arbitrary directions, thereby generalizing previous work by the authors.