J
2020
The Wave-Front Equation of Gravitational Signals in Classical General Relativity
CREMASCHINI, Claudio a Massimo TESSAROTTO
Základní údaje
Originální název
The Wave-Front Equation of Gravitational Signals in Classical General Relativity
Vydání
Symmetry, 2020, 2073-8994
Další údaje
Typ výsledku
Článek v odborném periodiku
Obor
10300 1.3 Physical sciences
Stát vydavatele
Švýcarsko
Utajení
není předmětem státního či obchodního tajemství
Kód RIV
RIV/47813059:19630/20:A0000087
Organizační jednotka
Fyzikální ústav v Opavě
Klíčová slova anglicky
General Relativity Hamilton equations; General Relativity Hamilton-Jacobi theory; wave-front theory; speed of propagation
Příznaky
Mezinárodní význam, Recenzováno
V originále
In this paper the dynamical equation for propagating wave-fronts of gravitational signals in classical general relativity (GR) is determined. The work relies on the manifestly-covariant Hamilton and Hamilton-Jacobi theories underlying the Einstein field equations recently discovered (Cremaschini and Tessarotto, 2015-2019). The Hamilton-Jacobi equation obtained in this way yields a wave-front description of gravitational field dynamics. It is shown that on a suitable subset of configuration space the latter equation reduces to a Klein-Gordon type equation associated with a 4-scalar field which identifies the wave-front surface of a gravitational signal. Its physical role and mathematical interpretation are discussed. Radiation-field wave-front solutions are pointed out, proving that according to this description, gravitational wave-fronts propagate in a given background space-time as waves characterized by the invariant speed-of-light c. The outcome is independent of the actual shape of the same wave-fronts and includes the case of gravitational waves which are characterized by an eikonal representation and propagate in a generic curved space-time along a null geodetics. The same waves are shown: (a) to correspond to the geometric-optics limit of the same curved space-time solutions; (b) to propagate in a flat space-time as plane waves with constant amplitude; (c) to display also the corresponding form of the wave-front in curved space-time. The result is consistent with the theory of the linearized Einstein field equations and the existence of gravitational waves achieved in such an asymptotic regime. Consistency with the non-linear Trautman boundary-value theory is also displayed.
Zobrazeno: 25. 12. 2024 07:16