Bose-Einstein condensates with derivative and long-range interactions as set-ups for analog black holes

General types of Bose-Einstein condensates are considered. The formation of black-hole analogues is examined for both short- and long-range interactions for arbitrary spatial dimensions greater than 2. The former case includes nonlinear derivative terms plus an inevitable external potential, while the latter one consists solely of gravitylike self-interactions for which intrinsic formation of analogue Schwarzschild-type background space-times is possible. The corresponding geometries are studied, and it is shown how they can be made stable. Their Hawking temperature is estimated, and it is found that in certain setups it can be significantly increased, thus providing better detectability.

Figure 1

$r_{*}$ as a function of $\beta$ for three different spatial dimensions $d$ (3, 4, 5; bottom to top). The other parameters are $\alpha =m=n_0=|v_{00}|=U_0=1$.

Figure 2

Particle-number density $n_0(r)$ (red, dashed) and velocity $|v_0(r)|$ (green, dot-dashed) for $d=3$ (upper respective graphs) and $d=4$ (lower respective graphs) for $r_{\max }=5\times 10^4$, $m=10^{-1}$, $|v_{00}|=10^{-2}$, and $C=10^{-4}$.

Figure 3

Metric component $g_{00}(r)$ for various values of $r_{\max }$ ($10^3$, $10^4$, $10^5$; left to right). The other parameters are $d=3$, $m=10^{-1}$, $|v_{00}|=10^{-2}$, and $C=10^{-4}$.