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Lense-Thirring Acoustic Black Holes : Shadows and Light

We introduce the Lense-Thirring Acoustic Black Hole (LTABH), motivated by the relevance of analogue models for black holes embedded in various physical systems, such as the cosmological microwave background or quantum superfluids. We investigate the LTABH spacetime geometry, showing that the roots of the metric function determine a partition of the spacetime into four regions, depending on the acoustic parameter $ξ$ (whereas the dependence vanishes for the rotation parameter $a$); on the other hand, the parameter $a$ turns out to affect the critical radii associated to the maxima of the effective potential. All in all, both the acoustic sphere radius $r_{as}$ and the photon sphere radius $r_{ps}$, respectively giving rise to the acoustic shadow $R_{as}$ and to the optical shadow $R_{s}$, depend on $ξ$ and $a$. More precisely, the rotation parameter $a$ is more relevantly affecting $R_{s}$ (through a right shift), while $R_{as}$ retains its circular shape. For what concerns the acoustic parameter, we notice that the higher $ξ$ is, the larger the size of both shadows. All of these results are confirmed through a detailed analysis of the distortions and of the shadows radii. Moreover, by deriving the magnitude of the precession frequency $Ω$, we observe that it significantly increases near the acoustic horizons, both in the extremal and in the non-extremal cases, which implies that the Lense-Thirring (frame dragging) effect, which can be traced back to $ξ$ itself, becomes important near such regions. On the other hand, we also show that there are regions of the LTABH spacetime in which $% Ω$ vanishes, suggesting that therein possible probe particles would not be affected by the frame dragging at all. Finally, we derive the deflection of the light near the LTABH.