Rotating sonic black hole from Spin-orbit coupled Bose-Einstein condensate

We show that a sonic analogue of rotating BTZ type of black hole can be realised in a quasi-two-dimensional spin-orbit coupled BEC without any external rotation. The corresponding equation for phase fluctuations in total density mode that describes phonon field in hydrodynamic approximation, is described by a scalar field equation in 2+1 dimension whose space-time metric can be identified with the space-time metric of rotating black hole of BTZ type. By time evolving the condensate in a suitably created laser induced potential, we show that the the moving condensate forms such rotating black hole in an annular region bounded by inner and outer event horizon as well as elliptical ergo surfaces. We discuss the self amplifying density modulations as well as the distribution of supersonic and subsonic zones in such rotating black hole that strongly depends on the spin-orbit coupled anisotropy that can be tested in experiments. We also calculate the density-density correlation in such analogue rotating black hole and the distribution of the analogue Hawking temperature on the event horizon