As shown by the development of Special Relativity the simultaneity concept should be related to that of reference frame. Poincare' proposed to define the simultaneity of two events by means of light signals following what is nowadays known as the Einstein simultaneity convention. The need of a simultaneity definition is present also in general relativity and in curved spacetimes in order to provide the observers with a coordinate time. It is recognized that the old Einstein simultaneity convention is nothing but a connection on a suitable trivial bundle that defines the reference frame. Unfortunately, it has a non vanishing holonomy in curved and even in flat spacetimes a fact that makes it almost useless. We point out the advantage of local simultaneity conventions showing that they are represented by local simultaneity connections. Among them there is one, uniquely determined by the reference frame, which is particularly well-behaved globally.

Spacelike slices from globally well-behaved simultaneity connections / E. Minguzzi. - STAMPA. - (2007), pp. 179-184. ((Intervento presentato al convegno XXVII Spanish Relativity Meeting 'Beyond General Relativity' tenutosi a Miraflores de la Sierra, Madrid nel 23-25 settembre 2004.

Spacelike slices from globally well-behaved simultaneity connections

MINGUZZI, ETTORE
2007

Abstract

As shown by the development of Special Relativity the simultaneity concept should be related to that of reference frame. Poincare' proposed to define the simultaneity of two events by means of light signals following what is nowadays known as the Einstein simultaneity convention. The need of a simultaneity definition is present also in general relativity and in curved spacetimes in order to provide the observers with a coordinate time. It is recognized that the old Einstein simultaneity convention is nothing but a connection on a suitable trivial bundle that defines the reference frame. Unfortunately, it has a non vanishing holonomy in curved and even in flat spacetimes a fact that makes it almost useless. We point out the advantage of local simultaneity conventions showing that they are represented by local simultaneity connections. Among them there is one, uniquely determined by the reference frame, which is particularly well-behaved globally.
Beyond general relativity : proceedings of the 2004 Spanish Relativity Meeting (ERE2004)
XXVII Spanish Relativity Meeting 'Beyond General Relativity'
Miraflores de la Sierra, Madrid
23-25 settembre 2004
E. Minguzzi
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2158/16737
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