Vertical stability of circular orbits in relativistic razor-thin disks

Autor(es)

Vieira, Ronaldo S. S. ; Ramos-Caro, Javier ; Saa, Alberto

• Tipo de documento: Artigo Científico
• Fonte: PHYSICAL REVIEW D; v. 94, n. 10, p. 13-pg., 2016-11-07.

Resumo

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)

• Processo FAPESP: 10/00487-9 - Estudo dinâmico de sistemas autogravitantes newtonianos e pós-newtonianos com matéria escura
• Beneficiário: Ronaldo Savioli Sumé Vieira
• Modalidade de apoio: Bolsas no Brasil - Doutorado
• Processo FAPESP: 09/16304-3 - Modelos posnewtonianos de sistemas autogravitantes
• Beneficiário: Javier Fernando Ramos Caro
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado
• Processo FAPESP: 15/10577-9 - Caos e integrabilidade em discos galácticos
• Beneficiário: Ronaldo Savioli Sumé Vieira
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado
• Processo FAPESP: 13/09357-9 - Física e geometria do espaço-tempo
• Beneficiário: Alberto Vazquez Saa
• Modalidade de apoio: Auxílio à Pesquisa - Temático