Curvature dependence of relativistic epicyclic frequencies in static, axially symmetric spacetimes
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Curvature dependence of relativistic epicyclic frequencies in static, axially symmetric spacetimes
Original language description
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) > 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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10308 - Astronomy (including astrophysics,space science)
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Physical Review D
ISSN
2470-0010
e-ISSN
2470-0029
Volume of the periodical
95
Issue of the periodical within the volume
4
Country of publishing house
US - UNITED STATES
Number of pages
6
Pages from-to
'044008-1'-'044008-6'
UT code for WoS article
000393512400005
EID of the result in the Scopus database
2-s2.0-85021878771