The Wave-Front Equation of Gravitational Signals in Classical General Relativity

@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 a Massimo TESSAROTTO. The Wave-Front Equation of Gravitational Signals in Classical General Relativity. \textit{Symmetry}. 2020, roč.~12, č.~2, s.~''216-1''-''216-25'', 25 s. ISSN~2073-8994. Dostupné z: https://dx.doi.org/10.3390/sym12020216.