New aspect of critical nonlinearly charged black hole

The motion of a point charged particle moving in the background of the critical power Maxwell charged AdS black holes in a probe approximation is studied. The extended phase space, where the cosmological constant appears as a pressure, is regarded and the effective potential is investigated. At last, the mass-to-charge ratio and the large $q$ limit are studied.

Figure 1

$V_{\mathrm{eff}}(r)$ versus $r$ for $L=0$ and $q=10$, and $D=6$ black (bold line), $D=7$ black (solid line), $D=8$ red (dotted line), $D=9$ blue (dashed line) and $D=10$ green (dash-dotted line) with $s=0.9$ (upper panel), $s=1$ (middle panel) and $s=1.2$ (lower panel).

Figure 2

$V_{\mathrm{eff}}(r)$ versus $r$ for $L=0$ and $D=4$, and $q=10$ black (bold line), $q=30$ red (solid line), $q=50$ blue (dotted line) and $q=70$ green (dashed line) with $s=0.9$ (upper panel), $s=1$ (middle panel) and $s=1.2$ (lower panel).

Figure 3

mass-to-charge ratio($\frac{M_{cr}}{Q}$) in respect to nonlinearity parameter(s),for different dimensions. The red (solid line), blue (dotted line), green (dash-dotted line) and black (dashed line) lines are $D=4$, $D=6$, $D=8$ and $D=10$, respectively. The right and the left figure is the case of $q=100$ and $q=10$, respectively.

Figure 4

$q_{\mathrm{eff}}$ versus $s$ for $q=1$, $D=4$ (left panel), $D=5$ (right panel), and $r=0.1$ (solid line), $r=1$ (bold line), $r=1.5$ (dotted line) and $r=5$ (dashed line).