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Lynden-Bell D.,Institute of Astronomy | Lynden-Bell D.,Racah Institute of Physics
Classical and Quantum Gravity | Year: 2014

When a static cylindrical system is subjected to equal and opposite torques top and bottom it transports angular momentum along its axis. The external metric of this static system can be transformed to Levi-Civita's form by using helical coordinates. This gives the external metric of a static cylinder three dimensionless parameters corresponding to the mass per unit length, the total stress along the cylinder, and the total torque. The external vacuum metric of a spherical system is characterised by its mass alone. How many parameters characterise the external metric of a general stationary cylindrical system? Leaving aside the radius of the cylinder which defines the scale we find that there are five parameters, the three above mentioned, to which should be added the momentum along the cylinder per unit length and the angular momentum per unit length. We show how to transform Levi-Civita's one parameter metric to include all five. © 2014 IOP Publishing Ltd.

Lynden-Bell D.,Institute of Astronomy | Katz J.,Institute of Astronomy | Katz J.,Racah Institute of Physics
Monthly Notices of the Royal Astronomical Society | Year: 2014

Large contributions to the near closure of the Universe and to the acceleration of its expansion are due to the gravitation of components of the stress-energy tensor other than its mass density. To familiarize astronomers with the gravitation of these components we conduct thought experiments on gravity, analogous to the real experiments that our forebears conducted on electricity. By analogy to the forces due to electric currents we investigate the gravitational forces due to the flows of momentum, angular momentum and energy along a cylinder. Under tension the gravity of the cylinder decreases but the 'closure' of the 3-space around it increases. When the cylinder carries a torque the flow of angular momentum along it leads to a novel helical interpretation of Levi-Civita's external metric and a novel relativistic effect. Energy currents give gravomagnetic effects in which parallel currents repel and antiparallel currents attract, though such effects must be added to those of static gravity. The gravity of beams of light give striking illustrations of these effects and a re-derivation of light bending via the gravity of the light itself. Faraday's experiments lead us to discuss lines of force of both gravomagnetic and gravity fields. A serious conundrum arises if Landau and Lifshitz's definition of gravitational force is adopted. © 2014 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society.

Katz J.,Racah Institute of Physics | Katz J.,Institute of Astronomy | Lynden Bell D.,Institute of Astronomy | Bicak J.,Institute of Astronomy | And 2 more authors.
Classical and Quantum Gravity | Year: 2011

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. © 2011 IOP Publishing Ltd.

Lynden-Bell D.,Institute of Astronomy | Bicak J.,Institute of Astronomy | Bicak J.,Charles University | Katz J.,Institute of Astronomy | Katz J.,Racah Institute of Physics
Classical and Quantum Gravity | Year: 2012

A new formula is given for the fast linear gravitational dragging of the inertial frame within a rapidly accelerated spherical shell of deep potential. The shell is charged and is electrically accelerated by an electric field whose sources are included in the solution.

Lynden-Bell D.,Institute of Astronomy | Katz J.,Institute of Astronomy | Katz J.,Racah Institute of Physics
Classical and Quantum Gravity | Year: 2012

In electromagnetism a current along a wire tightly wound on a torus makes a solenoid whose magnetic field is confined within the torus. In Einstein's gravity we give a corresponding solution in which a current of matter moves up on the inside of a toroidal shell and down on the outside, rolling around the torus by the short way. The metric is static outside the torus but stationary inside with the gravomagnetic field confined inside the torus, running around it by the long way. This exact solution of Einstein's equations is found by fitting Bonnor's solution for the metric of a light beam, which gives the required toroidal gravomagnetic field inside the torus, to the general Weyl static external metric in toroidal coordinates, which we develop. We deduce the matter tensor on the torus and find when it obeys the energy conditions. We also give the equipotential shells that generate the simple BachWeyl metric externally and find which shells obey the energy conditions. © 2012 IOP Publishing Ltd.

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