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

Abstract

Abstract 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 $$\theta =0$$ θ=0 . Also we show that the emergent black hole metrics are satisfying Einstein’s equations for large r and $$\theta =0$$ θ=0 . Our analysis is done in the context of dark energy in an emergent gravity scenario having $$k-$$ k- essence scalar fields $$\phi $$ ϕ with a Dirac–Born–Infeld type Lagrangian. In KN and KNAdS background, the scalar field $$\phi (r,t)=\phi _{1}(r)+\phi _{2}(t)$$ ϕ(r,t)=ϕ1(r)+ϕ2(t) satisfies the emergent gravity equations of motion at $$r\rightarrow \infty $$ r→∞ for $$\theta =0$$ θ=0 .