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.

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.

typ: | article |
---|---|

journal: | Class. Quantum Grav. |

volume: | 28 |

pages: | 065004 |

year: | 2011 |

pacs: | 04.20.-q |