Exact solutions of nonlocal gravity in a class of almost universal spacetimes

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F21%3A00544036" target="_blank" >RIV/67985840:_____/21:00544036 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1103/PhysRevD.103.124067" target="_blank" >https://doi.org/10.1103/PhysRevD.103.124067</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1103/PhysRevD.103.124067" target="_blank" >10.1103/PhysRevD.103.124067</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Exact solutions of nonlocal gravity in a class of almost universal spacetimes

Popis výsledku v původním jazyce

We study exact solutions of the infinite derivative gravity with null radiation which belong to the class of almost universal Weyl type III/N Kundt spacetimes. This class is defined by the property that all rank-2 tensors Bab constructed from the Riemann tensor and its covariant derivatives have traceless part of type N of the form B(...)Sab and the trace part constantly proportional to the metric. Here, B(...) is an analytic operator and Sab is the traceless Ricci tensor. We show that the convoluted field equations reduce to a single nonlocal but linear equation, which contains only the Laplace operator Δ on 2-dimensional spaces of constant curvature. Such a nonlocal linear equation is always exactly solvable by eigenfunction expansion or using the heat kernel method for the nonlocal form factor exp(-ℓ2Δ) (with ℓ being the length scale of nonlocality) as we demonstrate on several examples. We find the nonlocal analogues of the Aichelburg-Sexl and the Hotta-Tanaka solutions, which describe gravitational waves generated by null sources propagating in Minkowski, de Sitter, and anti-de Sitter spacetimes. They reduce to the solutions of the local theory far from the sources or in the local limit, ℓ→0. In the limit ℓ→∞, they become conformally flat. We also discuss possible hints suggesting that the nonlocal solutions are regular at the locations of the sources in contrast to the local solutions, all curvature components in the natural null frame are finite and specifically the Weyl components vanish.

Název v anglickém jazyce

Exact solutions of nonlocal gravity in a class of almost universal spacetimes

Popis výsledku anglicky

We study exact solutions of the infinite derivative gravity with null radiation which belong to the class of almost universal Weyl type III/N Kundt spacetimes. This class is defined by the property that all rank-2 tensors Bab constructed from the Riemann tensor and its covariant derivatives have traceless part of type N of the form B(...)Sab and the trace part constantly proportional to the metric. Here, B(...) is an analytic operator and Sab is the traceless Ricci tensor. We show that the convoluted field equations reduce to a single nonlocal but linear equation, which contains only the Laplace operator Δ on 2-dimensional spaces of constant curvature. Such a nonlocal linear equation is always exactly solvable by eigenfunction expansion or using the heat kernel method for the nonlocal form factor exp(-ℓ2Δ) (with ℓ being the length scale of nonlocality) as we demonstrate on several examples. We find the nonlocal analogues of the Aichelburg-Sexl and the Hotta-Tanaka solutions, which describe gravitational waves generated by null sources propagating in Minkowski, de Sitter, and anti-de Sitter spacetimes. They reduce to the solutions of the local theory far from the sources or in the local limit, ℓ→0. In the limit ℓ→∞, they become conformally flat. We also discuss possible hints suggesting that the nonlocal solutions are regular at the locations of the sources in contrast to the local solutions, all curvature components in the natural null frame are finite and specifically the Weyl components vanish.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA19-09659S" target="_blank" >GA19-09659S: Přesná řešení teorií gravitace: černé díry, zářivé prostoročasy a elektromagnetická pole</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2021

Kód důvěrnosti údajů

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

Název periodika

Physical Review D

ISSN

2470-0010

e-ISSN

2470-0029

Svazek periodika

103

Číslo periodika v rámci svazku

12

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

19

Strana od-do

124067

Kód UT WoS článku

000669042800014

EID výsledku v databázi Scopus

2-s2.0-85109031768