Abstract
This work is focused on the geometrical and physical characteristics of the class of reference frames associated to harmonic coordinates. Precisely, we express in relative form the harmonicity conditions and consider the so called “spatially harmonicity” of a reference frame in spherical symmetry. The initial data problem is then analyzed in polar coordinates and the obtained results are applied to special cases of exact solutions.
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References
Arzelies H.: Le champ statique à symmetrie spherique, pp. 16–20. Gauthier–Villars, Paris (1963)
Bochicchio I.: On the restricted evolution problem of Einstein relativistic mechanics. Ric. Mat. 59(2), 327–341 (2010). doi:10.1007/s11587-010-0090-9
Bochicchio I.: Existence and physical uniqueness of the restricted evolution problem of the Einstein relativistic mechanics. Ric. Mat. 60(2), 179–192 (2011). doi:10.1007/s11587-010-0100-y
Caricato G.: Translation of absolute evolutions laws of a continuous system in one comoving physical frame of reference. Some exact solutions. Int. J. Pure Appl. Math. 59(1), 19–37 (2010)
Caricato G.: Sur le problème de Cauchy pour les equations de la relativitè generale dans les schèmas materièls fluid parfait et matiere pure. Annales de l’Institut Henri Poincarè 9(3), 283–301 (1968)
Caricato G.: Il problema ristretto di evoluzione per un fluido perfetto carico di elettricità. Ric. Mat. 25, 51–80 (1975)
Cattaneo C.: Introduzione alla teoria einsteiniana della gravitazione, 2. Libreria Eredi Virgilio Veschi, Roma (1962)
Cattaneo C.: Proiezioni naturali e derivazione trasversa in una varietà riemanniana a metrica iperbolica normale. Ann. Mat. Pura Appl. 48, 361 (1959)
Fock V.: Einstenian Static in Conformal Space. Recent Developments in General Relativity, pp. 209–223. Pergamon Press, Oxford (1962)
Fourès-Bruhat Y.: Théoréme d’ existence pour certain systémes d’ équations aux dériveés partielles nonlinéaires. Acta Mat. 88, 141–225 (1952)
Fourès-Bruhat Y.: Théorémes d’ existence en mécanique des fluides relativistes. Bull. Soc. Math. France 86, 155–175 (1958)
Graif F.: Sull’uso di coordinate armoniche in relatività generale, Atti Accademia dei Lincei. Rend. Sci. Fis. Nat. 34, 312–320 (1963)
Laserra E.: Una particolare proprietà delle equazioni di Einstein. Rendiconti di Matematica, Roma 9, 335–346 (1989)
Laserra E.: Relative formulation of the relativistic Cauchy problem for a charged continuum. J. Inf. Optim. Sci. 22(1), 23–34 (2001)
Lichnerowicz A.: Theories Relativistes de la Gravitation et de l’Electromagnetisme. Masson and Cie, Paris (1955)
Longobardi A., Mazziotti E.: On geometrical and physical consequences of using certain special classes of comoving physical frames of reference. J. Interdiscip. Math. 12(6), 883–900 (2009)
Longobardi A., Mazziotti E.: On geometrical and physical consequences of using certain special classes of comoving physical frames of reference II. J. Interdiscip. Math. 14(2), 189–204 (2011)
Synge J.L.: Relativity: The General Theory. North-Holland Publishing Company, Amsterdam (1960)
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Bochicchio, I., Laserra, E., Longobardi, A. et al. Reference frames in harmonic coordinates: geometric and physical aspects. Ricerche mat. 61, 219–230 (2012). https://doi.org/10.1007/s11587-011-0125-x
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DOI: https://doi.org/10.1007/s11587-011-0125-x