Thought experiments on gravitational forces

Abstract

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.