The Hawking temperature in the context of dark energy

Abstract

An emergent gravity metric incorporating k−essence scalar fields φ 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 φemergent be solutions of the emergent gravity equations of motion under cosmological boundary conditions at ∞, then for r → ∞ the rescaled field φemergent 2GM −1 has exact correspondence with φ with φ(r, t) = φ1(r)+φ2(t). The Hawking temperature of this metric is Temergent =h c 3 8πGM k B (1 − K) 2 ≡h 8πGM k B (1 − K) 2 , taking the speed of light c = 1. Here K =φ 2 2 is the kinetic energy of the k−essence field φ and K is always less than unity, kB is the Boltzmann constant. This is phenomenologically interesting in the context of Belgiorno et al's gravitational analogue experiment.

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

“…In [1] this was shown for an emergent gravity metricG μν having k-essence scalar fields φ with a Born-Infeld type lagrangian and with the gravitational metric as Schwarzschild. The lagrangian for k-essence scalar fields contain non-canonical kinetic terms.…”

“…In [1] it has been shown that the Hawking temperature [2][3][4][5][6][7][8][9][10][11][12][13][14] is modified in the presence of dark energy. In [1] this was shown for an emergent gravity metricG μν having k-essence scalar fields φ with a Born-Infeld type lagrangian and with the gravitational metric as Schwarzschild.…”

“…In Ref. [1] this was shown by mapping the emergent gravity metric (having Schwarzschild background) into a BarriolaVilenkin black hole metric which again satisfies the Einstein equations. Here we find that for the case of an RN background the emergent gravity metric can be exactly mapped onto a Robinson-Trautman black hole so that the Einstein equations are automatically satisfied.…”

Thermodynamics for the k-essence emergent Reissner–Nordstrom–de Sitter spacetime

“…Barriola-Velenkin, Robinson-Trautman (RT) type spacetimes [6,7] and for the Kerr, Kerr-Newman and Kerr-Newman-AdS background, the emergent metrics are satisfying Einstein equation for large r along θ = 0 [7,8]. Also, in the above references, the authors have established the modification of the Hawking temperature [30]- [44] in the presence of dark energy in an emergent gravity scenario.…”

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

“…The Lagrangian for k−essence scalar fields contains non-canonical kinetic terms. The general form of the Lagrangian for k−essence model is: L = −V (φ)F (X) where X = 1 2 g µν ∇ µ φ∇ ν φ and it does not depend explicitly on φ to start with [2,3,5,6].Relativistic field theories with canonical kinetic terms have the distinction from those with non-canonical kinetic terms associated with k−essence, since the nontrivial dynamical solutions of the k-essence equation of motion not only spontaneously break Lorentz invariance but also change the metric for the perturbations around these solutions. Thus the perturbations propagate in the so called emergent or analogue curved spacetime [5] with the metric different from the gravitational one.…”