Publikace ÚTF

Starting from the gravitational potential of a Newtonian spheroidal shell we
discuss electrically charged rotating prolate spheroidal shells in the Maxwell
theory. In particular we consider two confocal charged shells which rotate
oppositely in such a way that there is no magnetic field outside the outer shell.
In the Einstein theory we solve the Ernst equations in the region where the
long prolate spheroids are almost cylindrical; in equatorial regions the exact
Lewis ‘rotating cylindrical’ solution is so derived by a limiting procedure from
a spatially bound system. In the second part we analyze two cylindrical shells
rotating in opposite directions in such a way that the static Levi-Civita metric
is produced outside and no angular momentum flux escapes to infinity. The
rotation of the local inertial frames in flat space inside the inner cylinder is
thus exhibited without any approximation or interpretational difficulties within
this model. A test particle within the inner cylinder kept at rest with respect
to axes that do not rotate as seen from infinity experiences a centrifugal force.
Although in suitably chosen axes the spacetime there is exactly Minkowskian
out to the inner cylinder, nevertheless, those inertial frame axes rotate with
respect to infinity, so relative to the inertial frame inside the inner cylinder a
test particle is traversing a circular orbit.