Centrifugal force induced by relativistically rotating spheroids and cylinders

TL;DR

This paper investigates the effects of relativistic rotation on spacetime and inertial frames using models of rotating spheroids and cylinders, revealing how centrifugal forces can arise in flat spacetime due to relativistic rotation.

Contribution

It provides exact solutions for rotating spheroidal and cylindrical shells in Einstein's theory, demonstrating how rotation influences local inertial frames without approximations.

Findings

Rotation induces inertial frame dragging effects.

Centrifugal forces can be experienced in flat spacetime due to relativistic rotation.

Exact solutions illustrate the rotation of local inertial frames in relativistic models.

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.