Aspects of Gauss-Bonnet scalarisation of charged black holes
Abstract
The general relativity vacuum black holes (BHs) can be scalarised in models where a scalar field non-minimally couples to the Gauss-Bonnet (GB) invariant. Such GB scalarisation comes in two flavours, depending on the GB sign that triggers the phenomenon. Hereafter these two cases are termed GB scalarisation. For vacuum BHs, only GB+ scalarisation is possible in the static case, while GB- scalarisation is spin induced. But for electrovacuum BHs, GB- is also charged induced. We discuss the GB- scalarisation of Reissner-Nordstr\"om and Kerr-Newman BHs, discussing zero modes and constructing fully non-linear solutions. Some comparisons with GB+ scalarisation are given. To assess the generality of the observed features, we also briefly consider the GB scalarisation of stringy dilatonic BHs and coloured BHs which provide qualitative differences with respect to the electrovacuum case.
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