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Annali di Matematica Pura ed Applicata

, Volume 117, Issue 1, pp 311–337 | Cite as

Relative continuum mechanics in general relativity

I. — Kinematical foundations
  • Enrico Massa
Article

Summary

An axiomatic approach to relative continuum kinematics in General Relativity is proposed. In the space-time manifold ϑ4, we consider a physical frame of reference [Γ], and a congruence ξ of world-lines, interpreted as the congruence of stream-lines of an ideal physical system ℬ. The kinematical and geometrical properties of ξ relative to [Γ] are then analysed on the basis of the following scheme: a) definition and group theoretical interpretation of the class C(ξ) of connection vectors associated with ξ; b) spatial resolution of C(ξ), and construction of the velocity gradient of ξ relative to [Γ]; c) analysis of the time-dependent metric concepts associated with ξ in the frame of reference [Γ] (spatial distances between neighbouring world-lines, spatial volumes, Lorentz contractions, etc.).

Keywords

General Relativity Geometrical Property Physical System Velocity Gradient Spatial Distance 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Sunto.

Si propone un approccio assiomatico allo studio della cinematica relativa dei continui in Relatività Generale. Nello spazio-tempo ϑ4 è assegnato un sistema di riferimento [Γ], e una congruenza ξ di linee di universo, pensata come la congruenza di linee di corrente di un sistema fisico ideals ℬ. Vengono quindi analizzate le proprietà cinematiche e geometriche di ξ relative al riferimento [Γ], sulla base del seguente schema: a) definizione e caratterizzazione in termini gruppali della classe C(ξ) dei vettori di connessione associati alla congruenza ξ; b) risoluzione spaziale di C(ξ), e costruzione del gradiente di velocità di ξ relativo a [Γ]; c) analisi delle proprietà metriche dipendenti dal tempo della congruenza ξ nel riferimento [Γ] (distanze spaziali tra linee di universo contigue, volumi spaziali, contrazioni di Lorentz, etc.).

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Copyright information

© Nicola Zanichelli Editore 1978

Authors and Affiliations

  • Enrico Massa
    • 1
  1. 1.Genova

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