The Hawking temperature in the context of dark energy for Kerr\u2013Newman and Kerr\u2013Newman\u2013AdS backgrounds

Goutam Manna,Bivash Majumder

doi:10.1140/epjc/s10052-019-7066-z

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 rrightarrow infty for theta =0.

Highlights

Research on the context of the Hawking temperature has gained momentum during last two decades
It has been shown that the Hawking temperature [1,2,3,4,5,6,7,8,9,10,11,12] is modified in the presence of dark energy in an emergent gravity scenario for Schwarzschild, Reissner–Nordstrom and Kerr background in [13,14]
As seen in [13,14], for an emergent gravity metric Gμν is conformally transformed into Gμν where Gμν = gμν − ∂μφ∂νφ for Dirac–Born–Infeld(DBI) [15,16,17] type Lagrangian having φ as k−essence scalar field

Summary

Introduction

Research on the context of the Hawking temperature has gained momentum during last two decades. We calculate the Hawking temperature for emergent gravity metric for Kerr– Newman and Kerr–Newman–AdS backgrounds using tunneling mechanism. These temperatures are different from usual temperatures of Kerr–Newman and Kerr–Newman– AdS black holes. 2, we have described k-essence and emergent gravity where the metric Gμν contains the dark energy field φ and this field should satisfy the emergent gravity equations of motion. 3 and 5, we have shown that for Kerr–Newman and Kerr–Newman–AdS both cases, the emergent gravity metrics are mapped on to the Kerr–Newman and Kerr– Newman–AdS type metrics in the presence of dark energy.

Kerr–Newman metric and emergent gravity

The Hawking temperature for KN type metric in the presence of dark energy

Kerr–Newman–AdS background

The Hawking temperature for KNAdS type metric in the presence of dark energy

Conclusion