Curvature dependence of relativistic epicyclic frequencies in static, axially symmetric spacetimes

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19240%2F17%3AA0000059" target="_blank" >RIV/47813059:19240/17:A0000059 - isvavai.cz</a>

Výsledek na webu

<a href="https://journals.aps.org/prd/abstract/10.1103/PhysRevD.95.044008" target="_blank" >https://journals.aps.org/prd/abstract/10.1103/PhysRevD.95.044008</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1103/PhysRevD.95.044008" target="_blank" >10.1103/PhysRevD.95.044008</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Curvature dependence of relativistic epicyclic frequencies in static, axially symmetric spacetimes

Popis výsledku v původním jazyce

The sum of squared epicyclic frequencies of nearly circular motion (omega^(2)_(r) + omega^(2)_(theta)) in axially symmetric configurations of Newtonian gravity is known to depend both on the matter density and on the angular velocity profile of circular orbits. It was recently found that this sum goes to zero at the photon orbits of Schwarzschild and Kerr spacetimes. However, these are the only relativistic configurations for which such a result exists in the literature. Here, we extend the above formalism in order to describe the analogous relation for geodesic motion in arbitrary static, axially symmetric, asymptotically flat solutions of general relativity. The sum of squared epicyclic frequencies is found to vanish at photon radii of vacuum solutions. In the presence of matter, we obtain that omega^(2)_(r) + omega^(2)_(theta) &gt; 0 for perturbed timelike circular geodesics on the equatorial plane if the strong energy condition holds for the matter-energy fluid of spacetime; in vacuum, the allowed region for timelike circular geodesic motion is characterized by the inequality above. The results presented here may be of use to shed light on general issues concerning the stability of circular orbits once they approach photon radii, mainly the ones corresponding to stable photon motion.

Název v anglickém jazyce

Curvature dependence of relativistic epicyclic frequencies in static, axially symmetric spacetimes

Popis výsledku anglicky

The sum of squared epicyclic frequencies of nearly circular motion (omega^(2)_(r) + omega^(2)_(theta)) in axially symmetric configurations of Newtonian gravity is known to depend both on the matter density and on the angular velocity profile of circular orbits. It was recently found that this sum goes to zero at the photon orbits of Schwarzschild and Kerr spacetimes. However, these are the only relativistic configurations for which such a result exists in the literature. Here, we extend the above formalism in order to describe the analogous relation for geodesic motion in arbitrary static, axially symmetric, asymptotically flat solutions of general relativity. The sum of squared epicyclic frequencies is found to vanish at photon radii of vacuum solutions. In the presence of matter, we obtain that omega^(2)_(r) + omega^(2)_(theta) &gt; 0 for perturbed timelike circular geodesics on the equatorial plane if the strong energy condition holds for the matter-energy fluid of spacetime; in vacuum, the allowed region for timelike circular geodesic motion is characterized by the inequality above. The results presented here may be of use to shed light on general issues concerning the stability of circular orbits once they approach photon radii, mainly the ones corresponding to stable photon motion.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10308 - Astronomy (including astrophysics,space science)

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2017

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

95

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

6

Strana od-do

'044008-1'-'044008-6'

Kód UT WoS článku

000393512400005

EID výsledku v databázi Scopus

2-s2.0-85021878771