The Hawking Temperature in the context of Dark Energy for Reissner-Nordstrom and Kerr background

Abstract: For emergent gravity metrics, presence of dark energy modifies the Hawking temperature. We show that for the spherically symmetric Reissner-Nordstrom (RN) background metric, the emergent metric can be mapped into a Robinson-Trautman blackhole. Allowed values of the dark energy density follow from rather general conditions. For some allowed value of the dark energy density this blackhole can have zero Hawking temperature i.e. the blackhole does not radiate. For a Kerr background along $\theta=0$, the emergent blackhole metric satisfies Einstein's equations for large $r$ and always radiates. Our analysis is done in the context of emergent gravity metrics having $k-$essence scalar fields $\phi$ with a Born-Infeld type lagrangian. In both cases the scalar field $\phi(r,t)=\phi_{1}(r)+\phi_{2}(t)$ also satisfies the emergent gravity equations of motion for $r\rightarrow\infty$ and $\theta=0$. \keywords{dark energy, k-essence, Reissner-Nordstrom and Kerr blackholes} \pacs{98.80.-k ;95.36.+x}