Dirac quasinormal frequencies of Schwarzschild-anti-de Sitter and Reissner-Nordstrom-anti-de Sitter black holes

We investigate the Dirac quasinormal modes (QNMs) of the Schwarzschild-anti-de Sitter and Reissner-Nordstrom-anti-de Sitter (SAdS/RNAdS) black holes using Horowitz-Hubeny approach. For large black holes, the fundamental QNMs are the linear functions of the Hawking temperature, and the slope of the lines decreases as the charge increases. For intermediate and small SAdS black holes, the real part of the fundamental QNMs approximates a temperature curve but the corresponding imaginary part is almost a linear function of the radius of the black hole. The quasinormal frequencies for high overtones become evenly spaced and the spacings are related to the mass and charge of the black hole. We also study the relation between QNMs and angular quantum number and find that the quasinormal frequencies increase as the angular quantum number increases.

Figure 1

Graphs of fundamental QNMs versus $T/r_{+}$ for the SAdS black holes. The left panel is drawn for large black holes and right one for intermediate and small black holes.

Figure 2

Graphs of fundamental QNMs versus $T$ for RNAdS black holes with $\lambda =1$.

Figure 3

Graphs of $\omega$ with $Q/Q_{\mathrm{ext}}$ for $n=0,3,5$, $r_{+}=100$ and $\lambda =1$. The left three figures are drawn for $\mathrm{Re}(\omega )$. The right figures are for $\mathrm{Im}(\omega )$ in which the continuous lines describe the oscillatory modes and the dashed lines show the nonoscillatory modes.

Figure 4

Graphs of $\omega (n)/r_{+}$ versus $n$ for $\lambda =1$, $r_{+}=100$ and $Q=0.1Q_{\mathrm{ext}},0.3Q_{\mathrm{ext}},0.5Q_{\mathrm{ext}},0.6Q_{\mathrm{ext}}$. The dashed lines describe $\mathrm{Re}(\omega (n))/r_{+}$ and the solid lines are $\mathrm{Im}(\omega (n))/r_{+}$.

Figure 5

Graphs of the increment $dW$ with $\lambda$ (or $l$) for $n=0,2,4,6,8$ and $Q=0.1Q_{\mathrm{ext}},0.3Q_{\mathrm{ext}}$. The left two figures are drawn for $dW=\mathrm{Re}(\omega (l,n))-\mathrm{Re}(\omega (0,n))$ and the right two are for $dW=-\mathrm{Im}(\omega (l,n))+\mathrm{Im}(\omega (0,n))$.