  We make use of the Lagrangian description of fluid motion to highlight
certain features in the context of spacetime geometry as emergent phenomena in
fluid systems. By using Lagrangian Perturbation Theory (LPT), we find that if
the flow is not barotropic it will not be locally irrotational, and as a
result, emergent gravity can not be realised for such flow. Our work gives a
new perspective of examining the perturbations in a fluid from a different
approach (other than Eulerian approach) which is the way of using Lagrangian
Perturbation Theory. We make use of Lagrangian description of motion to examine
the propagation of Eikonal wave (wave having very short wavelength) from the
reference frame of the observer moving with the background flow. We find that
waves of ultra short wavelength propagate similar to waves in a static uniform
medium in the near vicinity of the observer. We restrict ourselves to
nonrelativistic flows in astrophysical black hole accretion.
