Aspects of Gauss-Bonnet Scalarisation of Charged Black Holes
Carlos Herdeiro, Alexandre M. Pombo, Eugen Radu
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-Nordström 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, namely on the distribution and existence of regions triggering GB− scalarisation.