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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10300 - Physical sciences

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2020

Kód důvěrnosti údajů

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

Název periodika

Symmetry

ISSN

2073-8994

e-ISSN

—

Svazek periodika

12

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

25

Strana od-do

„216-1“-„216-25“

Kód UT WoS článku

000521147600031

EID výsledku v databázi Scopus

2-s2.0-85080863786