Cosmological constant and AdS spacetimes from Minkowski spheres

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27120%2F22%3A10250361" target="_blank" >RIV/61989100:27120/22:10250361 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.worldscientific.com/doi/10.1142/S0219887822501146" target="_blank" >https://www.worldscientific.com/doi/10.1142/S0219887822501146</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1142/S0219887822501146" target="_blank" >10.1142/S0219887822501146</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Cosmological constant and AdS spacetimes from Minkowski spheres

Popis výsledku v původním jazyce

A theory of gravity without masses can be constructed starting from Minkowski M-(p,M-q) spaces. The corresponding adapted (p, q) Minkowski potentials, gradients and Laplacians built on each signature lead to a field equation similar to the Newton-Laplace one. In this framework, the anti-de Sitter spacetime is a hypersurface described by a constant potential of Minkowski gravitational force in absence of matter. We show that the cosmological constant of the anti-de Sitter spacetimes is related to a geometric property of Minkowski spheres: the centro-affine conservation of volumes defined from the so-called Minkowski-Tzizteica affine spheres. It is possible to show the connection between the anti-de Sitter AdS(2, 3) space, the non-Euclidean geometry and the difference between Minkowski M-(2,M-3) sphere and the pseudosphere seen as a surface of the 3-Euclidean space. According to a suitable parameterization, the relation between de Sitter and anti-de Sitter spacetimes in any dimension is fixed. As a consequence, the light can travel in any anti-de Sitter spacetime defining the geodesic structure. These considerations can be recast in terms of Einstein field equations with cosmological constant and extended to f(R) gravity.

Název v anglickém jazyce

Cosmological constant and AdS spacetimes from Minkowski spheres

Popis výsledku anglicky

A theory of gravity without masses can be constructed starting from Minkowski M-(p,M-q) spaces. The corresponding adapted (p, q) Minkowski potentials, gradients and Laplacians built on each signature lead to a field equation similar to the Newton-Laplace one. In this framework, the anti-de Sitter spacetime is a hypersurface described by a constant potential of Minkowski gravitational force in absence of matter. We show that the cosmological constant of the anti-de Sitter spacetimes is related to a geometric property of Minkowski spheres: the centro-affine conservation of volumes defined from the so-called Minkowski-Tzizteica affine spheres. It is possible to show the connection between the anti-de Sitter AdS(2, 3) space, the non-Euclidean geometry and the difference between Minkowski M-(2,M-3) sphere and the pseudosphere seen as a surface of the 3-Euclidean space. According to a suitable parameterization, the relation between de Sitter and anti-de Sitter spacetimes in any dimension is fixed. As a consequence, the light can travel in any anti-de Sitter spacetime defining the geodesic structure. These considerations can be recast in terms of Einstein field equations with cosmological constant and extended to f(R) gravity.

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

2022

Kód důvěrnosti údajů

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

Název periodika

International Journal of Geometric Methods in Modern Physics

ISSN

0219-8878

e-ISSN

1793-6977

Svazek periodika

19

Číslo periodika v rámci svazku

08

Stát vydavatele periodika

SG - Singapurská republika

Počet stran výsledku

28

Strana od-do

"nestrankovano"

Kód UT WoS článku

000812255500012

EID výsledku v databázi Scopus

2-s2.0-85129110516