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

## TL;DR

This paper investigates how dark energy influences the Hawking temperature of Kerr-Newman and Kerr-Newman-AdS black holes within an emergent gravity framework, revealing modifications to temperature and solutions satisfying Einstein's equations at large distances.

## Contribution

It introduces a novel analysis of Hawking temperature modifications due to dark energy in emergent gravity for specific black hole backgrounds, including explicit calculations along the axis.

## Key findings

- Hawking temperature is altered by dark energy in emergent gravity.
- Emergent metrics satisfy Einstein's equations at large r and along θ=0.
- Scalar fields behave consistently with emergent gravity equations at infinity.

## 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 $\theta=0$. 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 $\phi$ with a Dirac-Born-Infeld type lagrangian. In KN and KNAdS background, the scalar field $\phi(r,t)=\phi_{1}(r)+\phi_{2}(t)$ satisfies the emergent gravity equations of motion at $r\rightarrow\infty$ for $\theta=0$.