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

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19630%2F20%3AA0000087" target="_blank" >RIV/47813059:19630/20:A0000087 - isvavai.cz</a>

Result on the web

<a href="https://www.mdpi.com/2073-8994/12/2/216" target="_blank" >https://www.mdpi.com/2073-8994/12/2/216</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.3390/sym12020216" target="_blank" >10.3390/sym12020216</a>

Result language

angličtina

Original language name

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

Original language description

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.

Czech name

—

Czech description

—

Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

10300 - Physical sciences

Project

—

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2020

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Symmetry

ISSN

2073-8994

e-ISSN

—

Volume of the periodical

12

Issue of the periodical within the volume

2

Country of publishing house

CH - SWITZERLAND

Number of pages

25

Pages from-to

„216-1“-„216-25“

UT code for WoS article

000521147600031

EID of the result in the Scopus database

2-s2.0-85080863786