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

Yiqian Chen,Qingyu Gan,Guangzhou Guo

Figure 2. The lowest-lying QNMs $-{\rm{Im}}(\omega )/{\kappa }_{-}$ of three families for a neutral massless scalar field. The vertical solid lines indicate that the parameters reach the lower bound of allowed region, where the logarithmic-dS black hole does not have three horizons. SCC is violated only when the dominant modes of three families are all above the red dashed line. And the thick black dashed lines indicate the key points where $\beta \equiv -{\rm{Im}}(\omega )/{\kappa }_{-}=\tfrac{1}{2}$. (a) The lowest-lying QNMs $-{\rm{Im}}(\omega )/{\kappa }_{-}$ of three families with varying $Q/{Q}_{\mathrm{ext}}$ for various values of b and Λ. The vertical thin dashed lines indicate that the NE modes become dominant. On the right side of the thick dashed lines, we can see that SCC is violated. (b) The lowest-lying QNMs $-{\rm{Im}}(\omega )/{\kappa }_{-}$ of three families with varying b for various values of $Q/{Q}_{\mathrm{ext}}$ and Λ. Near the vertical solid thin lines, we can see that SCC is always respected for a small enough value of b.