The Hawking temperature in the context of dark energy

An emergent-gravity metric incorporating k-essence scalar fields phi having a Born-Infeld-type Lagrangian is mapped into a metric whose structure is similar to that of a blackhole of large mass M that has swallowed a global monopole. However, here the field is not that of a monopole but rather that of a k-essence scalar field. If phi(emergent) are the solutions of the emergent-gravity equations of motion under cosmological boundary conditions at infinity, then for r -> infinity the rescaled field phi(emergent)/2GM-1 has exact correspondence with phi with phi(r, t) = phi(1)(r) + phi(2)(t). The Hawking temperature of this metric is T-emergent = (h) over barc(3)/8 pi GMk(B) (1 - K)(2) equivalent to (h) over bar /8 pi GMk(B) (1 - K)(2), taking the speed of light c = 1. Here K = (phi)over dot(2)(2) is the kinetic energy of the k-essence field phi and K is always less than unity, k(B) is the Boltzmann constant. This is phenomenologically interesting in the context of Belgiorno et al.'s gravitational analogue experiment. Copyright (C) EPLA, 2012