  The {\bf k-}essence emergent Reissner-Nordstrom-de Sitter spacetime has
exactly mapped on to the Robinson-Trautman (RT) type spacetime with
cosmological constant $\L$ for certain configuration of {\bf k-}essence scalar
field. Theoretically, we evaluated that the thermodynamical quantities for the
RT type emergent black hole is different from the usual one in the presence of
kinetic energy of the {\bf k-}essence scalar field i.e., the dark energy
density. We restrict ourselves into the fact that the dark energy density (K)
is to be unity, then the effective temperature and pressure both are negative
for the RT type emergent black hole which implies that the system is
thermodynamically unstable when the charge $Q\neq 0$ and the emergent spacetime
is only dark energy dominated and it does not radiate when $Q=0$. The
thermodynamically unstable situation is physically plausible only when we
consider spin degrees of freedom of a system. We have made this analysis in the
context of dark energy in an emergent gravity scenario having {\bf k-}essence
scalar fields $\phi$ with a Dirac-Born-Infeld type lagrangian. The scalar field
also satisfies the emergent equation of motion at $r\rightarrow\infty$.
