Spontaneous scalarization of charged black holes at the approach to extremality

Yves Brihaye; Betti Hartmann

doi:10.1016/j.physletb.2019.03.043

paper

Spontaneous scalarization of charged black holes at the approach to extremality

arXiv:1902.05760 · doi:10.1016/j.physletb.2019.03.043

Abstract

We study static, spherically symmetric and electrically charged black hole solutions in a quadratic Einstein-scalar-Gauss-Bonnet gravity model. Very similar to the uncharged case, black holes undergo spontaneous scalarization for sufficiently large scalar-tensor coupling $γ$ - a phenomenon attributed to a tachyonic instability of the scalar field system. While in the uncharged case, this effect is only possible for positive values of $γ$ , we show that for sufficiently large values of the electric charge $Q$ two independent domains of existence in the $γ$ - $Q$ -plane appear: one for positive $γ$ and one for negative $γ$ . We demonstrate that this new domain for negative $γ$ exists because of the fact that the near-horizon geometry of a nearly extremally charged black hole is $A d S_{2} \times S^{2}$ .This new domain appears for electric charges larger than approximately 74 $%$ of the extremal charge. For positive $γ$ we observe that a singularity with diverging curvature invariants forms outside the horizon when approaching extremality.

13 pages including 6 figures and one table

Spontaneous scalarization of charged black holes at the approach to extremality

Abstract

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