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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Vertical stability of circular orbits in relativistic razor-thin disks

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Vieira, Ronaldo S. S. ; Ramos-Caro, Javier ; Saa, Alberto
Total Authors: 3
Document type: Journal article
Source: Physical Review D; v. 94, n. 10 NOV 7 2016.
Web of Science Citations: 5

During the last few decades, there has been a growing interest in exact solutions of Einstein equations describing razor-thin disks. Despite the progress in this area, the analytical study of geodesic motion crossing the disk plane in these systems has not yet been well developed. In the present work, we propose a definite vertical stability criterion for circular equatorial timelike geodesics in static, axially symmetric thin disks, possibly surrounded by other structures preserving axial symmetry. It turns out that the strong energy condition for the disk stress-energy content is sufficient for the vertical stability of these orbits. Moreover, adiabatic invariance of the vertical action variable gives us an approximate third integral of motion for oblique orbits that deviate slightly from the equatorial plane. This new approximate third integral certainly points to a better understanding of the analytical properties of these orbits. The results presented here, derived for static spacetimes, may be a starting point to study the motion around rotating, stationary razor-thin disks. Our results also allow us to conjecture that the strong energy condition should be sufficient to assure transversal stability of periodic orbits for any singular timelike hypersurface, provided it is invariant under the geodesic flow. (AU)

FAPESP's process: 13/09357-9 - Physics and geometry of spacetime
Grantee:Alberto Vazquez Saa
Support type: Research Projects - Thematic Grants
FAPESP's process: 15/10577-9 - Chaos and integrability in galactic disks
Grantee:Ronaldo Savioli Sumé Vieira
Support type: Scholarships in Brazil - Post-Doctorate
Grantee:Javier Fernando Ramos Caro
Support type: Scholarships in Brazil - Post-Doctorate
FAPESP's process: 10/00487-9 - Dynamical study of Newtonian and post-Newtonian self-gravitating systems with dark matter
Grantee:Ronaldo Savioli Sumé Vieira
Support type: Scholarships in Brazil - Doctorate