On the stability of general relativistic geometric thin disks

Details On the stability of general relativistic geometric thin disks On the stability of general relativistic geometric thin disks

2004-09-28

arxiv.org/abs/gr-qc/0409110v1

Phys.Rev. D70 (2004) 084015

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

11 pages, RevTex. Phys Rev D (in press)

Scientific paper

10.1103/PhysRevD.70.084015

The stability of general relativistic thin disks is investigated under a general first order perturbation of the energy momentum tensor. In particular, we consider temporal, radial and azimuthal "test matter" perturbations of the quantities involved on the plane $z=0$. We study the thin disks generated by applying the "displace, cut and reflect" method, usually known as the image method, to the Schwarzschild metric in isotropic coordinates and to the Chazy-Curzon metric and the Zipoy-Voorhees metric ($\gamma$-metric) in Weyl coordinates. In the case of the isotropic Schwarzschild thin disk, where a radial pressure is present to support the gravitational attraction, the disk is stable and the perturbation favors the formation of rings. Also, we found the expected result that the thin disk models generated by the Chazy-Curzon and Zipoy-Voorhees metric with only azimuthal pressure are not stable under a general first order perturbation

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