arXiv subjects
Publications and source records attributed to H. Balasin.
We show that within the Ashtekar formulation of General Relativity a considerably simple and compact form of the Lorentzian Hamiltonian constraint occurs for a particular value of the Barbero--Immirzi parameter.
Exact stationary axially symmetric solutions of the 4D Einstein equations with corotating pressureless perfect fluid sources are studied. A particular solution with approximately flat rotation curve is discussed in some detail. We find that simple Newtonian arguments overestimate the amount of matter needed to explain these curves by more than 30%. The crucial insight gained by this model is that the Newtonian approximation breaks down globally, even though it is valid locally everywhere. No conflict with solar system tests arises.
The ultrarelativistic limit of twodimensional dilaton gravity is presented and its associated (anti-)selfdual energy momentum tensor is derived. It is localized on a null line, although the line element remains twice differentiable. Relations to the Aichelburg-Sexl spacetime and constant dilaton vacua are pointed out. Geodesics are found to be smooth for minimally coupled test particles but non-smooth -- with a finite jump in the acceleration -- for test particles coupled non-minimally to the dilaton. Quantization on boosted backgrounds is discussed; no anomalous trace of the energy momentum tensor arises and the 1-loop flux component can be adjusted to be equal to the classical flux of the shock wave.
We consider the head-on collision of two opposite-charged point particles moving at the speed of light. Starting from the field of a single charge we derive in a first step the field generated by uniformly accelerated charge in the limit of infinite acceleration. From this we then calculate explicitly the burst of radiation emitted from the head-on collision of two charges and discuss its distributional structure. The motivation for our investigation comes from the corresponding gravitational situation where the head-on collision of two ultrarelativistic particles (black holes) has recently aroused renewed interest.
We discuss the asymptotic structure of the ultrarelativistic Schwarzschild black hole. An explicit construction for a conformal boundary both at spatial and null infinity is given together with the corresponding expressions for the ADM and Bondi four-momenta.
We argue that it is possible to assign Bondi as well as ADM four-momentum to the ultrarelativistic limit of the Schwarzschild black hole in agreement to what is expected on physical grounds: The Bondi-momentum is lightlike and equal to the ADM-momentum up to the retarded time when particle and radiation escape to infinity and drops to zero thereafter, leaving flat space behind.
A general analysis of the gravitational dynamics of a medium with a continuous distribution of vorticity indicates that the answer to the question raised in the title is affirmative, contrary to a recent claim.
We generalize previous work on the energy-momentum tensor-distribution of the Kerr geometry by extending the manifold structure into the negative mass region. Since the extension of the flat part of the Kerr-Schild decomposition from one sheet to the double cover develops a singularity at the branch surface we have to take its non-smoothness into account. It is however possible to find a geometry within the generalized Kerr-Schild class that is in the Colombeau-sense associated to the maximally analytic Kerr-metric.
We extend the Colombeau algebra of generalized functions to arbitrary (infinitely differentiable, paracompact) n-dimensional manifolds M. Embedding of continuous functions and distributions is achieved with the help of a family of n-forms defined on the tangent bundle TM, which form a partition of unity upon integration over the fibres.
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 $θ(0)$. We show that this ambiguity may be resolved by imposing covariant constancy of the square of the tangent. Our result is consistent with Colombeau's multiplication of distributions.
We generalize previous \cite{AiBa2} work on the classification of ($C^\infty$) 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 the classification of (non-vacuum) pp-waves \cite{JEK} based on the Killing-algebra of the space-time by admitting distribution-valued profile functions. Our approach is based on the analysis of the (infinite-dimensional) group of ``normal-form-preserving'' diffeomorphisms.
It is shown that the metric of a massless particle obtained from boosting the Schwarzschild metric to the velocity of light, has four Killing vectors corresponding to an $E(2)\times \RR$ symmetry-group. This is in agreement with the expectations based on flat-space kinematics but is in contrast to previous statements in the literature \cite{Schueck}. Moreover, it also goes beyond the general Jordan-Ehlers-Kundt-(JEK)-classification of gravitational pp-waves as given in \cite{JEK}.