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

TL;DR

This paper explores the thermodynamics of a k-essence emergent Reissner-Nordstrom-de Sitter black hole, revealing negative temperature and pressure under certain conditions, indicating thermodynamic instability influenced by dark energy and scalar fields.

Contribution

It provides a novel analysis of thermodynamic properties of emergent black holes in k-essence gravity, highlighting instability due to dark energy dominance and scalar field effects.

Findings

Effective temperature and pressure are negative when dark energy density is unity.

The black hole system is thermodynamically unstable for non-zero charge.

No radiation occurs when the charge is zero.

Abstract

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 $r\rightarrow\infty$.