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

TL;DR

This paper investigates how dark energy influences the Hawking temperature of black holes in emergent gravity frameworks, showing conditions under which black holes can cease radiating or always radiate, depending on the background metric and dark energy density.

Contribution

It introduces a novel analysis of Hawking temperature modifications in emergent gravity metrics with dark energy for Reissner-Nordstrom and Kerr black holes, including conditions for zero temperature.

Findings

Reissner-Nordstrom black holes can have zero Hawking temperature with certain dark energy densities.

Kerr black holes always radiate at large distances in the studied framework.

Emergent gravity with k-essence scalar fields modifies black hole thermodynamics.

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}