Local simultaneity conventions are mathematically represented by connections on the bundle of timelike curves that defines the frame. Those simultaneity conventions having an holonomy proportional to the Riemann tensor have a special interest since they exhibit good global behaviour in the weak field limit. By requiring that the simultaneity convention depends on the acceleration, vorticity vector and the angle between them we are able to restrict considerably the allowed simultaneity conventions. In particular, we focus our study on the simplest among the allowed conventions. It should be preferred over Einstein's in flat spacetime and in general if the tidal force between neighbouring particles is weaker than the centrifugal force. It reduces to the Einstein convention if the vectorial product between the acceleration and the vorticity vector vanishes. We finally show how to use this convention in practice.
A globally well-behaved simultaneity connection for stationary frames in the weak field limit / Minguzzi, Ettore. - In: CLASSICAL AND QUANTUM GRAVITY. - ISSN 0264-9381. - STAMPA. - 21:(2004), pp. 4123-4146. [10.1088/0264-9381/21/17/007]
A globally well-behaved simultaneity connection for stationary frames in the weak field limit
MINGUZZI, ETTORE
2004
Abstract
Local simultaneity conventions are mathematically represented by connections on the bundle of timelike curves that defines the frame. Those simultaneity conventions having an holonomy proportional to the Riemann tensor have a special interest since they exhibit good global behaviour in the weak field limit. By requiring that the simultaneity convention depends on the acceleration, vorticity vector and the angle between them we are able to restrict considerably the allowed simultaneity conventions. In particular, we focus our study on the simplest among the allowed conventions. It should be preferred over Einstein's in flat spacetime and in general if the tidal force between neighbouring particles is weaker than the centrifugal force. It reduces to the Einstein convention if the vectorial product between the acceleration and the vorticity vector vanishes. We finally show how to use this convention in practice.I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.