Engelbert L Schucking

Motion of charged particles in homogeneous electromagnetic fields

An invariant geometrical description of the world lines of charged particles in arbitrary homogeneous electromagnetic fields is presented. This is accomplished through the combined use of the Frenet‐Serret equations and the Lorentz equation. The results apply to flat as well as Riemannian space‐time. The intrinsic scalars associated with these curves (i.e., their curvatures and first and second torsions) are found to be constants of the motion when they are well defined. Moreover, they form simple relationships with the field invariants as well as with the energy and momentum densities of the rest frame fields. When they are evaluated in the instantaneous rest frame of the particle, the Frenet vectors lend themselves to simple physical interpretation. It is shown that one cannot distinguish in an intrinsic geometrical manner between the curves of positive and negative charges. The same is true for positive and negative magnetic monopoles if they exist. In such a case, however, one would be able to disting...

“Golden Oldie”: The Bianchi Classification in the Schücking-Behr Approach

The historical development of the Bianchi classification of homogeneous cosmological models is described with special emphasis on the contributions by Schücking and Behr.

The rest frame in stationary space−times with axial symmetry

A rest frame in a stationary, axially symmetric space−time is defined as a synchronizable frame which is as nearly Killing as possible. This is a possible generalization of the Newtonian rest frame. A kinematical theorem giving the condition for the existence of a rest frame whose time vector is a linear combination of the Killing vectors is proved. The frame is also unique. The condition is shown to be weaker than the assumption of orthogonal transitivity. The surfaces of simultaneity of the rest frame are the surfaces of constancy of a particular Killing time coordinate, and its time vector is the component of the time Killing vector orthogonal to the angular Killing vector. Some properties of the rest frame are then discussed; it is shown that the frame is well−behaved down to the event horizon, where its time vector becomes null. Under a suitable condition on the event horizon, the time vector coincides with a Killing vector there. The gravitational redshift relation in the rest frame is derived. Ther...

Gödel’s trip

We discuss the geometrical light cone structure in Godel’s rigidly rotating cosmos and correct a picture in the standard literature.

Pressure as a source of gravity

The active mass density in Einsteins theory of gravitation in the analog of Poissons equation in a local inertial system is proportional to

Approaches to Gödel's rotating universe

\rho+3p/c^2

Redshifts and Killing vectors

. Here

Active mass under pressure

\rho

The world viewed from outside

is the density of energy and

Isometric embedding for homogeneous compact 3-manifolds

p