Scalar Deformations of Schwarzschild Holes and Their Stability

Details Scalar Deformations of Schwarzschild Holes and Their Stability Scalar Deformations of Schwarzschild Holes and Their Stability

1996-12-21

arxiv.org/abs/gr-qc/9612062v2

Int.J.Mod.Phys. A13 (1998) 741-764

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

24 pp, 16 figs, Latex; version published in Int. J. Mod. Phys. A

Scientific paper

10.1142/S0217751X98000329

We construct two solutions of the minimally coupled Einstein-scalar field equations, representing regular deformations of Schwarzschild black holes by a self-interacting, static, scalar field. One solution features an exponentially decaying scalar field and a triple-well interaction potential; the other one is completely analytic and sprouts Coulomb-like scalar hair. Both evade the no-hair theorem by having partially negative potential, in conflict with the dominant energy condition. The linear perturbation theory around such backgrounds is developed in general, and yields stability criteria in terms of effective potentials for an analog Schr\"odinger problem. We can test for more than half of the perturbation modes, and our solutions prove to be stable against those.

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