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

Thermodynamics for the k-essence Emergent Reissner-Nordstrom-de Sitter Spacetime