CREMASCHINI, Claudio and Massimo TESSAROTTO. The Wave-Front Equation of Gravitational Signals in Classical General Relativity. Symmetry. 2020, vol. 12, No 2, p. "216-1"-"216-25", 25 pp. ISSN 2073-8994. Available from: https://dx.doi.org/10.3390/sym12020216.
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Basic information
Original name The Wave-Front Equation of Gravitational Signals in Classical General Relativity
Authors CREMASCHINI, Claudio (380 Italy, belonging to the institution) and Massimo TESSAROTTO (380 Italy, belonging to the institution).
Edition Symmetry, 2020, 2073-8994.
Other information
Original language English
Type of outcome Article in a journal
Field of Study 10300 1.3 Physical sciences
Country of publisher Switzerland
Confidentiality degree is not subject to a state or trade secret
WWW URL
RIV identification code RIV/47813059:19630/20:A0000087
Organization unit Institute of physics in Opava
Doi http://dx.doi.org/10.3390/sym12020216
UT WoS 000521147600031
Keywords in English General Relativity Hamilton equations; General Relativity Hamilton-Jacobi theory; wave-front theory; speed of propagation
Tags FÚ, FÚ2020, RIV21
Tags International impact, Reviewed
Changed by Changed by: Mgr. Pavlína Jalůvková, učo 25213. Changed: 23/3/2021 22:10.
Abstract
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.
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