Harmonic oscillations of neutral particles in the γ metric

Bobir Toshmatov, Daniele Malafarina, Naresh Dadhich

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Abstract

We consider a well-known static, axially symmetric, vacuum solution of Einstein equations belonging to Weyl's class and determine the fundamental frequencies of small harmonic oscillations of test particles around stable circular orbits in the equatorial plane. We discuss the radial profiles of frequencies of the radial, latitudinal (vertical), and azimuthal (Keplerian) harmonic oscillations relative to the comoving and distant observers and compare with the corresponding ones in the Schwarzschild and Kerr geometries. We show that there exist latitudinal and radial frequencies of harmonic oscillations of particles moving along the circular orbits for which it is impossible to determine whether the central gravitating object is described by the slowly rotating Kerr solution or by a slightly deformed static space-time.

Original languageEnglish
Article number044001
JournalPhysical Review D
Volume100
Issue number4
DOIs
Publication statusPublished - Aug 1 2019

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ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)

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