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In the {\bf K-}essence Vaidya Schwarzschild spacetime, we apply the dynamicalhorizon equation to measure the mass-loss due to Hawking radiation and thetunneling formalism (Hamilton-Jacobi method) to calculate the hawkingtemperature. Assuming the Dirac-Born-Infeld kind of non-standard action for the{\bf K-}essence here, the background physical spacetime is a static sphericallysymmetric black hole, and we constrain the {\bf K-}essence scalar field to be afunction only of either forward or backward time. The {\bf K-}essence emergentgravity and the generalizations of Vaidya spacetime have been linked by Mannaet al. In this paper, we use Sawayama's modified description of the dynamicalhorizon to show that the obtained findings deviate from the standard Vaidyaspacetime geometry.

Evaporation of dynamical horizon with the Hawking temparature in the {\bf K-}essence emergent Vaidya spacetime