The Hawking temperature in the context of dark energy for Kerr-Newman and Kerr-Newman-AdS backgrounds

We show that the Hawking temperature is modified in the presence of dark energy in an emergent gravity scenario for Kerr-Newman(KN) and Kerr-Newman-AdS(KNAdS) background metrics. The emergent gravity metric is not conformally equivalent to the gravitational metric. We calculate the Hawking temperatures for these emergent gravity metrics along $\theta =0$. Also we show that the emergent black hole metrics are satisfying Einstein’s equations for large $r$ and $\theta =0$. Our analysis is done in the context of dark energy in an emergent gravity scenario having $k-$essence scalar fields $\varphi$ with a Dirac-Born-Infeld type lagrangian. In KN and KNAdS background, the scalar field $\varphi (r,t)={\varphi }_1(r)+{\varphi }_2(t)$ satisfies the emergent gravity equations of motion at $r\to \mathrm{\infty }$ for $\theta =0$.