Is the equivalence principle useful for understanding general relativity?

The Equivalence Principle (EP) is at the heart of General Relativity (GR), tested in many aspects. It is often used to discuss qualitatively the influence of gravity on physical phenomena. But can this be made more precise? We compare clock rates, frequency shifts, light deflection and time delay in simple static spacetimes to the analogous phenomena seen by accelerated observers in Minkowski space. In contrast to previous studies, we do not assume that the gravitational field is weak and see, as we proceed, how the field is constrained by the EP. Special care is taken that results are only observer-, but not coordinate-dependent. By this we clarify some of the issues raised in the literature and show which gravitational effects can and which cannot be simulated by acceleration. The paper may also serve as a contribution for critical discussions on the implications of the EP.Comment: 5 figure

Symmetries of pp-Waves with Distributional Profile

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.Comment: 10 pages, latex2e, no figures, statement about the combination of symmetry classes of impulsive waves correcte

Canonical Formulation of pp-waves

We construct a Hamiltonian formulation for the class of plane-fronted gravitational waves with parallel rays (pp-waves). Because of the existence of a light-like Killing vector, the dynamics is effectively reduced to a 2+1 evolution with "time" chosen to be light-like. In spite of the vanishing action this allows us to geometrically identify a symplectic form as well as dynamical Hamiltonian, thus casting the system into canonical form.Comment: To appear in the "Obregon Festschrift

ADM and Bondi four-momenta for the ultrarelativistic Schwarzschild black hole

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.Comment: Changes in the expression used for the ADM four-momentum without altering the result, correction of some minor typing error

A Note on the Symmetries of the Gravitational Field of a Massless Particle

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}.Comment: 10pages, amslatex, TUW-94-12 and UWThPh-1994-2

Generalized Symmetries of Impulsive Gravitational Waves

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.Comment: 18 pages, latex2e, no figure

Head-on collision of ultrarelativistic charges

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.Comment: 4 figures, uses the AMSmat