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@article{49446, author = {Cremaschini, Claudio and Tessarotto, Massimo}, article_number = {2}, doi = {http://dx.doi.org/10.3390/sym12020216}, keywords = {General Relativity Hamilton equations; General Relativity Hamilton-Jacobi theory; wave-front theory; speed of propagation}, language = {eng}, issn = {2073-8994}, journal = {Symmetry}, title = {The Wave-Front Equation of Gravitational Signals in Classical General Relativity}, url = {https://www.mdpi.com/2073-8994/12/2/216}, volume = {12}, year = {2020} }
TY - JOUR ID - 49446 AU - Cremaschini, Claudio - Tessarotto, Massimo PY - 2020 TI - The Wave-Front Equation of Gravitational Signals in Classical General Relativity JF - Symmetry VL - 12 IS - 2 SP - "216-1"-"216-25" EP - "216-1"-"216-25" SN - 20738994 KW - General Relativity Hamilton equations KW - General Relativity Hamilton-Jacobi theory KW - wave-front theory KW - speed of propagation UR - https://www.mdpi.com/2073-8994/12/2/216 N2 - 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. ER -
CREMASCHINI, Claudio and Massimo TESSAROTTO. The Wave-Front Equation of Gravitational Signals in Classical General Relativity. \textit{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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