Spontaneous scalarization of Gauss-Bonnet black holes surrounded by massive scalar fields

Abstract

For massless scalar fields, a relation $\hat{I}{”}_n=\frac{\sqrt{3}}{2}\ddot{I}€$ for $n\to \infty$ was observed in the scalar-Gauss-Bonnet theory. In the present paper, we extend the discussion by including a nonzero scalar field mass. For massive scalar fields, we show that the relation $\hat{I}{”}_n=\frac{\sqrt{3}}{2}\ddot{I}€$ for $n\to \infty$ still holds. We demonstrate this relation with both analytical and numerical methods. The analytical analysis implies that this relation may be a very universal behavior.

8 pages, 1 figure