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We study the properties of a $2+1$ dimensional Sonic black hole (SBH) thatcan be realised, in a quasi-two-dimensional two-component spin-orbit coupledBose-Einstein condensate (BEC). The corresponding equation for phasefluctuations in the total density mode that describes phonon field in thehydrodynamic approximation is described by a scalar field equation in $2+1$dimension whose space-time metric is significantly different from that of theSBH realised from a single component BEC that was studied experimentally, and,theoretically meticulously in literature. Given the breakdown of theirrotationality constraint of the velocity field in such spin-orbit coupledBEC, we study in detail how the time evolution of such condensate impacts thevarious properties of the resulting SBH. By time evolving the condensate in asuitably created laser-induced potential, we show that such a sonic black holeis formed, in an annular region bounded by inner and outer event horizon aswell as elliptical ergo-surfaces. We observe amplifying density modulation dueto the formation of such sonic horizons and show how they change the nature ofanalogue Hawking radiation emitted from such sonic black hole by evaluating thedensity-density correlation at different times, using the truncated Wignerapproximation (TWA) for different values of spin-orbit coupling parameters. Wefinally investigate the thermal nature of such analogue Hawking radiation.

(2+1)$-dimensional sonic black hole from spin-orbit coupled Bose-Einstein condensate and its analogue Hawking radiation