Greybody factors for a minimally coupled scalar field in a three-dimensional Einstein-power-Maxwell black hole background

In the present work we study the propagation of a probe minimally coupled scalar field in Einstein-power-Maxwell charged black hole background in ($1+2$) dimensions. We find analytical expressions for the reflection coefficient as well as for the absorption cross section in the low energy regime, and we show graphically their behavior as functions of the frequency for several values of the free parameters of the theory.

Figure 1

The effective potential as a function of the tortoise coordinate $V(x)$ assuming $m=0$ for three different cases: (i) $M=1.0$ and $Q=0.33$ (solid black line), (ii) $M=1.1$ and $Q=0.35$ (short dashed red line) and (iii) $M=1.2$ and $Q=0.37$ (long dashed blue line).

Figure 2

The reflection coefficient $\mathcal{R}$ as a function of the frequency $\omega$ assuming $m=1$ for three different cases as follows (from bottom to top): (i) $M=140$ and $Q=9.22\times {10}^4$ (solid red line), (ii) $M=145$ and $Q=9.02\times {10}^4$ (dashed blue line) and (iii) $M=150$ and $Q=8.82\times {10}^4$ (dotted green line).

Figure 3

The greybody factor ${\sigma }_m$ as a function of the frequency $\omega$ assuming $m=1$ for three different cases as follows: (from top to bottom) (i) $M=140$ and $Q=9.22\times {10}^4$ (solid red line), (ii) $M=145$ and $Q=9.02\times {10}^4$ (dashed blue line) and (iii) $M=150$ and $Q=8.82\times {10}^4$ (dotted green line).