Acoustic Black Hole in Hayward Spacetime: Shadow, Quasinormal Modes and Analogue Hawking Radiation

Abstract

In this paper, we study an acoustic black hole in Hayward spacetime from the relativistic Gross-Pitaevskii theory. By examining the critical null geodesics, the shadow of the acoustic horizon is sketched. Then the quasinormal mode (QNM) frequencies of the acoustic Hayward black hole are computed numerically using the WKB method, which are shown to be more stable than those of the Hayward black hole, and the variations in the QNM frequencies are shown to correlate with the behavior of the effective potential. Moreover, the WKB method is also employed to calculate the grey-body factor and energy emission rate of the analogue Hawking radiation. It is shown that, as the tuning parameter increases, both the grey-body factor and the energy emission rate are enhanced, which can likewise be attributed to changes in the effective potential. Besides, the radius of acoustic shadow increases with the tuning parameter as well. Our results not only construct an acoustic black hole in regular black hole spacetime, but may also provide potential applications in future observations of astrophysical black holes.

Figures (12)

• Figure 1: Horizon structure of the acoustic Hayward black hole. Left panel: Radii of the outer acoustic horizon $r_+'$, inner acoustic horizon $r_-'$, and Hayward horizon $r_{\text{H}}$ as functions of $L$, with fixed $\xi=5$. The vertical dashed line indicates the critical value $L=\sqrt{2}L_0$. Right panel: The same horizon radii as functions of $\xi$ for a fixed $L=L_0$. The vertical dashed line marks the critical value $\xi=4$.
• Figure 2: Schematic of the acoustic black hole shadow. The central gray circle denotes the acoustic black hole, surrounded by an acoustic sphere (yellow circle) of radius $r_\text{A}$. Null geodesics emitted from the observer on the right are grouped into three families: blue trajectories captured by the acoustic black hole; green trajectories escape after deflection; and red critical geodesics that determine the acoustic shadow between the captured and escaping paths.
• Figure 3: Acoustic black hole shadow and associated radii as functions of $\xi$ at fixed $L=L_0$. Acoustic shadow radius $r_\text{S}$, acoustic sphere radius $r_\text{A}$, acoustic horizon $r_+'$, and the second largest acoustic sphere radius $r_{\text{A}2}$ are plotted starting from the critical value $\xi=4$.
• Figure 4: Acoustic shadow patterns for different values of $\xi$ and $L$. Left panel: $L=L_0$ is fixed. Right panel: $\xi =5$ is fixed, with an inserted magnified view of a local region.
• Figure 5: Effective potential $V(r)$ as a function of the radial coordinate $r$ for several values of the tuning parameter $\xi$, with $L=L_0$ fixed. Left panel: $l=0$ is fixed. Right panel: $l=1$ is fixed.