Searching for non-minimally coupled scalar hairs

Details Searching for non-minimally coupled scalar hairs Searching for non-minimally coupled scalar hairs

1996-02-29

arxiv.org/abs/gr-qc/9602061v1

Phys.Rev.D53:7377-7380,1996

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Revtex, 10 pages

Scientific paper

10.1103/PhysRevD.53.7377

In this work we study the asymptotically flat, static, and spherically symmetric black-hole solutions of the theory described by the action $$S = \int d^nx\sqrt{-g} \left\{\left(1-\xi\phi^2 \right)R - g^{\mu\nu}\partial_\mu\phi\partial_\nu\phi\right\},$$ with $n>3$ and arbitrary $\xi$. We demonstrate the absence of scalar hairs for $\xi<0$. For $\xi>\xi_c=\frac{n-2}{4(n-1)}$, we show that there is no scalar hair obeying $|\phi(r)| < 1/\sqrt{\xi}$ or $|\phi(r)| > 1/\sqrt{\xi}$. For $0<\xi<\xi_c$, we prove the absence of scalar hairs such that $|\phi(r)| < 1/\sqrt{\xi}$ or $\frac{1}{\xi} < \phi^2(r) < \frac{\xi_c}{\xi(\xi_c-\xi)}$.

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