Strong cosmic censorship for a scalar field in a logarithmic-de Sitter black hole

Yiqian Chen,Qingyu Gan,Guangzhou Guo

Figure 1. Parameter space for logarithmic-ds black holes with M = 16π. (a) Λ = 0.02. (b) Λ = 0.14. The pink region allows for black holes with three horizons. The dashed green lines represent the extremal black holes with r− = r+; the dashed black line represents the Nariai black hole with r+ = rc; and the dashed red lines represent the constraint bQ3 = k. We can see the dashed red line and the dashed green line intersect at the point $P({b}_{\min },{Q}_{\max })$. Here, ${b}_{\min }\approx 0.206\,008$ and ${Q}_{\max }\approx 1.213\,543$ are calculated by numerical method which does not depend on Λ (an analytic expression will be given in the section 4). The blue line represent near-extremal black holes with charge Q = 0.9Qext, where Qext is the charge of a extremal black hole with the same b.