Exact Solutions and Scalar Fields in Gravity - Instituto Avanzado de ...

ON ELECTROMAGNETIC THIRRING
PROBLEMS
Markus King
Institute of Theoretical Physics
University of Tübingen, D–72076 Tübingen, Germany
Herbert Pfister
Institute of Theoretical Physics
University of Tübingen, D–72076 Tübingen, Germany
Keywords: Thirring problem, exact solutions.
1. INTRODUCTION
The standard Thirring problem describes the (non–local) influence
of rotating masses on the inertial properties of space–time, especially
the so–called dragging of inertial frames inside a rotating mass shell
relative to the asymptotic frames. It is then a natural question to ask
whether and how properties other than inertial ones are also influenced
by rotating masses, and the first (non–inertial and non–gravitational)
properties which come here to one’s mind, are surely electromagnetic
phenomena.
Indeed there exists a whole series of papers [1, 2, 3, 4, 5] on models
where a charge sits inside a slowly rotating mass shell (mass M, radius
R), and where the rotationally induced magnetic field is calculated and
discussed, typically for small ratios M/R and/or An especially
remarkable but confusing fact is that Cohen’s results [2] are in complete
agreement with Machian expectations whereas Ehlers and Rindler [4]
interpret their results to be “in fact Mach–negative or, at best, Mach–
neutral”.
We examine a class of models consisting of two spherical shells of radii
and the first one carrying a nearly arbitrary charge but no
rest mass, the second one being nearly arbitrary massive but electrically
neutral. The only restriction on the parameters is that the systems
should be free of singularities and horizons. To these shells we apply
small but otherwise arbitrary “stirring” angular velocities and
Exact Solutions and Scalar Fields in Gravity: Recent Developments
Edited by Macias et al., Kluwer Academic/Plenum Publishers, New York, 2001 281