Lense-Thirring Acoustic Black Holes : Shadows and Light

TL;DR

This work introduces the Lense–Thirring acoustic black hole (LTABH) as a slowly rotating analogue spacetime and analyzes its horizon structure, null geodesics, and optical/acoustic shadows. By deriving the LTABH metric from a relativistic Gross–Pitaevskii framework, the authors show that the acoustic parameter $\xi$ governs acoustic horizons and shadow sizes, while the rotation parameter $a$ chiefly shifts the optical shadow and modulates frame-dragging effects. They identify two distinct shadows—the optical shadow linked to the photon sphere and the acoustic shadow tied to the acoustic sphere—whose radii grow with $\xi$ and exhibit different sensitivities to $a$. Through a Gauss–Bonnet treatment of light deflection and a detailed precession analysis, they demonstrate enhanced frame dragging near acoustic horizons and regions where dragging can vanish, underscoring LTABH as a fruitful analogue platform for Kerr-like phenomena and horizon physics.

Abstract

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.

Figures (8)

• Figure 1: Left: Profile of the metric function F(r) with its roots for different values of the parameter $\xi$. Right: The roots as a function of the parameter $\xi$. The green region represents the non allowed values of $\xi$, i.e $\xi < 4$. We take $M=1$.
• Figure 2: Effective potential for different values of the acoustic parameter $\xi$ and different values of the rotating parameter $a$. The black curve is associated to the LTBH black hole. We take $M=1$, $E=\mathcal{K}=1$ and $L=20$.
• Figure 3: Roots of the effective potential derivative against the acoustic parameter $\xi$. The red dashed curve is associated to photon sphere radius of the LTBH black hole. We take $M=1$, $E=\mathcal{K}=1$ and $L=20$.
• Figure 4: Shadow radius as a function of the effective potential extrema against the acoustic parameter $\xi$. The red dashed curve is associated to photon sphere radius of the LTBH black hole for which $R_s=3\sqrt{3}M$. We take $M=1$, $E=\mathcal{K}=1$ and $L=20$.
• Figure 5: Left: Regular shadow $R_s\left( r_{ps} \right)$. Right: Acoustic shadow $R_s\left( r_{as} \right)$. We consider for these illustrations different values of the acoustic parameter $\xi$, the spin $a$ and a fixed black hole mass $\left( M=1 \right)$.