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General Relativity and Quantum Cosmology, gr-qc
Abstract:
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 the spacetime there is Minkowskian out to the inner cylinder
nevertheless that space has been induced to rotate, so relative to the local
inertial frame the particle is traversing a circular orbit.
