Eur. Phys. J. C (2014) 74: 2811
https://doi.org/10.1140/epjc/s10052-014-2811-9

Regular Article - Theoretical Physics

The Hawking temperature in the context of dark energy for Reissner–Nordstrom and Kerr background

¹ Department of Physics, Prabhat Kumar College, Contai, Purba Medinipur, 721401, West Bengal, India
² Department of Physics, Ramakrishna Mission Vivekananda University, P.O.-Belur Math, Howrah, 711202, West Bengal, India

^* e-mail: debashis@rkmvu.ac.in

Received: 19 January 2014
Accepted: 5 March 2014
Published online: 18 March 2014

Abstract

For emergent gravity metrics, the presence of dark energy modifies the Hawking temperature. We show that for the spherically symmetric Reissner–Nordstrom background metric, the emergent metric can be mapped into a Robinson–Trautman black hole. Allowed values of the dark energy density follow from rather general conditions. For some allowed values of the dark energy density this black hole can have zero Hawking temperature, i.e. the black hole does not radiate. For a Kerr background along , the emergent black hole metric satisfies Einstein’s equations for large and always radiates. Our analysis is done in the context of emergent gravity metrics having -essence scalar fields with a Born–Infeld type lagrangian. In both cases the scalar field also satisfies the emergent gravity equations of motion for and .