Electrically charged black holes in linear and nonlinear electrodynamics: Geodesic analysis and scalar absorption

Along the last decades, several regular black hole (BH) solutions, i.e., singularity-free BHs, have been proposed and associated to nonlinear electrodynamics models minimally coupled to general relativity. Within this context, it is of interest to study how those nonlinear-electrodynamic-based regular BHs (RBHs) would interact with their astrophysical environment. We investigate the propagation of a massless test scalar field in the background of an electrically charged RBH solution, obtained by Eloy Ayón-Beato and Alberto García. Using a numerical approach, we compute the absorption cross section of the massless scalar field for arbitrary values of the frequency of the incident wave. We compare the absorption cross sections of the Ayón-Beato and García RBH with the Reissner-Nordström BH, showing that they can be very similar in the whole frequency regime.

Figure 1

Comparison between the metric functions of ABG and RN BHs, as a function of $r$, for different choices of the normalized charge. The colored circles represent the location of the horizons in each case.

Figure 2

The horizons of ABG and RN BHs for distinct choices of the normalized charge. We also plot the function $f^{\mathrm{ABG}}(r)=f^{\mathrm{RN}}(r)$. The central inset shows the plots near the extreme charge value. Notice that there is a discontinuity at $\alpha =1$, for the plot $f^{\mathrm{ABG}}(r)=f^{\mathrm{RN}}(r)$.

Figure 3

The electrostatic fields of ABG and RN BHs, as a function of $r$, for different values of the normalized charge.

Figure 4

The critical radius (top panel) and the critical impact parameter (bottom panel) of ABG and RN BHs as functions of the normalized charge.

Figure 5

The effective potential of massless and chargeless scalar waves in the background of the ABG RBH: (i) as a function of $r$ for different choices of $l$, with $\alpha =0.5$ (left panel); and (ii) as a function of $r_{\star }$ with $l=0$, for different choices of the normalized charge (right panel).

Figure 6

The ACS of the ABG RBH for a massless chargeless scalar field divided by its area, as a function of $\omega$, considering the monopole mode ($l=0$) and different values of the normalized charge.

Figure 7

The horizon area of ABG, Bardeen and RN BHs as a function of the normalized charge.

Figure 8

The Lyapunov exponent of ABG and RN BHs, as functions of the normalized charged.

Figure 9

The total ACS of the ABG RBH for different values of the normalized charge as a function of $\omega$. In the top panel we exhibit the corresponding GCSs (horizontal dot-dashed lines), while in the bottom panel we exhibit the corresponding sinc approximation (dot-dashed lines).

Figure 10

The total ACS of the ABG RBH for different values of normalized charge as a function of $\omega$.

Figure 11

The partial ACS of the ABG RBH for different values of normalized charge as a function of $\omega$.

Figure 12

The partial ACSs of ABG and RN BHs for different values of normalized charge as a function of $\omega$.

Figure 13

The total ACSs of ABG and RN BHs for two selected values of the normalized charge as a function of $\omega$.

Figure 14

The values of the normalized charges for which the GCSs of ABG and RN BHs are equal.

Figure 15

The total ACSs for some pairs $({\alpha }^{\mathrm{ABG}},{\alpha }^{\mathrm{RN}})$ as a function of $\omega$.