  We study the properties of a $2+1$ dimensional Sonic black hole (SBH) that
can be realised, in a quasi-two-dimensional two-component spin-orbit coupled
Bose-Einstein condensate (BEC). The corresponding equation for phase
fluctuations in the total density mode that describes phonon field in the
hydrodynamic approximation is described by a scalar field equation in $2+1$
dimension whose space-time metric is significantly different from that of the
SBH realised from a single component BEC that was studied experimentally, and,
theoretically meticulously in literature. Given the breakdown of the
irrotationality constraint of the velocity field in such spin-orbit coupled
BEC, we study in detail how the time evolution of such condensate impacts the
various properties of the resulting SBH. By time evolving the condensate in a
suitably created laser-induced potential, we show that such a sonic black hole
is formed, in an annular region bounded by inner and outer event horizon as
well as elliptical ergo-surfaces. We observe amplifying density modulation due
to the formation of such sonic horizons and show how they change the nature of
analogue Hawking radiation emitted from such sonic black hole by evaluating the
density-density correlation at different times, using the truncated Wigner
approximation (TWA) for different values of spin-orbit coupling parameters. We
finally investigate the thermal nature of such analogue Hawking radiation.
