Charged scalar and Dirac perturbations on a global monopole Reissner-Nordström-de Sitter black hole: quasinormal modes and strong cosmic censorship

Abstract

We study perturbations of charged scalar and Dirac fields around Reissner-Nordström-de Sitter black holes with a global monopole. To this end, we first derive the equations of motion for both fields on the aforementioned background; these equations are then reformulated uniformly into the Teukolsky equation. Since the Teukolsky equation in asymptotically de Sitter spacetimes can be mapped into the Heun equation, we are able to solve quasinormal spectra by employing the Heun function method, not only for photon sphere modes but also for de Sitter and near-extremal modes. We analyze the spectra of all three types for both fields and, in particular, ascertain the effects of the global monopole. In the near-extremal regime, we find that the presence of a global monopole, on the one hand, leaves the strong cosmic censorship conjecture unaffected for scalar perturbations, while on the other hand, it enhance the violation of strong cosmic censorship for Dirac perturbations. Furthermore, we identify that the impact of the global monopole on both the spectra and the strong cosmic censorship is achieved by a shift in the modified multipole number. Our work demonstrates that the Heun function method is an efficient and robust approach for exploring the interaction between asymptotically de Sitter black holes and perturbing fields.

Figures (10)

• Figure 1: Real (left) and imaginary (right) parts of the fundamental quasinormal frequencies for scalar (top) and Dirac (bottom) fields in terms of $Q/Q_{\textit{max}}$, with $e=0$ and $\ell=1$ ($\ell=1/2$) for scalar (Dirac) fields. Note that here the blue, red and purple curves correspond to the PS, dS and NE modes, and the solid (dash-dotted) lines stand for $\eta^2=0$ ($\eta^2=0.2$).
• Figure 2: Real (left) and imaginary (right) parts of the fundamental PS frequencies for scalar (solid) and Dirac (dash-dotted) fields in terms of the monopole parameter $\eta^2$, with $e=0$, $Q=0.5$ and $\Lambda=0.06$. Note that here we have taken $\ell=0$ (blue) and $\ell=1$ (red) for scalar while $\ell=1/2$ (blue) and $\ell=3/2$ (red) for Dirac fields.
• Figure 3: Real (left) and imaginary (right) parts of the fundamental PS frequencies for scalar (solid) and Dirac (dash-dotted) fields in terms of the multipole number $\ell$, with the same parameters as in Fig. \ref{['fig:PS-1']}. Note that here we have taken various values of the monopole parameter, including $\eta^{2} = 0$ (red), $0.1$ (green), and $0.2$ (blue).
• Figure 4: Real (left) and imaginary (right) parts of the fundamental dS frequencies for scalar (solid) and Dirac (dash-dotted) fields in terms of the monopole parameter $\eta^2$, with $e=0.1$, $Q=0.5$ and $\Lambda=0.06$. Note that here we have taken $\ell=0$ (blue) and $\ell=1$ (red) for scalar while $\ell=1/2$ (blue) and $\ell=3/2$ (red) for Dirac fields.
• Figure 5: Real (left) and imaginary (right) parts of the fundamental dS frequencies for scalar (solid) and Dirac (dash-dotted) fields in terms of the multipole number $\ell$, with the same parameters as in Fig. \ref{['fig:dS-1']}. Note that here we have taken various values of the monopole parameter, including $\eta^{2} = 0$ (red), $0.1$ (green), and $0.2$ (blue).