The stable problem of the black-hole connected region in the Schwarzschild black hole

Details The stable problem of the black-hole connected region in the Schwarzschild black hole The stable problem of the black-hole connected region in the Schwarzschild black hole

2005-12-18

arxiv.org/abs/gr-qc/0512101v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

6 pages, no figures

Scientific paper

The stability of the Schwarzschild black hole is studied. Using the Painlev\'{e} coordinate, our region can be defined as the black-hole-connected region(r>2m, see text) of the Schwarzschild black hole or the white-hole-connected region(r>2m, see text) of the Schwarzschild black hole. We study the stable problems of the black-hole-connected region. The conclusions are: (1) in the black-hole-connected region, the initially regular perturbation fields must have real frequency or complex frequency whose imaginary must not be greater than -1/4m, so the black-hole-connected regionis stable in physicist' viewpoint; (2) On the contrary, in the mathematicians' viewpoint, the existence of the real frequencies means that the stable problem is unsolved by the linear perturbation method in the black-hole-connected region.

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