Acoustic geometry obtained through the perturbation of the Bernoulli's constant

For accretion onto astrophysical black holes, we demonstrate that linear perturbation of Bernoulli's constant defined for an inviscid irrotational adiabatic flow of perfect ideal fluid gives rise to phenomena of analogue gravity. The formulation of our work is done in the Newtonian framework and also within the General relativistic framework, i.e., considering a static spacetime background, as well. The resulting structure of the analogue acoustic metric is similar to the acoustic metric found in perturbing velocity potential and mass accretion rate.