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

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 θ = 0. Also we show that the emergent black hole metrics are satisfying Einstein's equations for large r and θ = 0. Our analysis is done in the context of dark energy in an emergent gravity scenario having k−essence scalar fields φ with a Dirac-Born-Infeld type lagrangian. In KN and KNAdS background, the scalar field φ(r, t) = φ1(r) + φ2(t) satisfies the emergent gravity equations of motion at r → ∞ for θ = 0. PACS numbers: 97.60.Lf; 98.80.-k ;95.36.+x I. INTRODUCTIONResearch on the context of the Hawking temperature has gained momentum during last two decades. It has been shown that the Hawking temperature [1] is modified in the presence of dark energy in an emergent gravity scenario for Schwarzschild, Reissner-Nordstrom and Kerr background in [2,3]. As seen in [2,3], for an emergent gravity metricG µν is conformally transformed intō G µν whereḠ µν = g µν − ∂ µ φ∂ ν φ (g µν is the gravitational metric) for Dirac-Born-Infeld(DBI) [4] type Lagrangian having φ as k−essence scalar field. 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. Relevant literatures [7] for such fields discuss about cosmology, inflation, dark matter, dark energy and strings.The motivation of this work is to calculate the Hawking temperature in the presence of dark energy for an emergent gravity metric which is also a blackhole metric. We consider two cases, (a) when the gravitational metric is a Kerr-Newman and (b) when the gravitational metric Kerr-Newman-AdS.In [10]- [21], discuss about Hawking radiation for Kerr, Kerr-Newman, Kerr-Newman-AdS etc. black holes using different techniques. Here 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.

Time-like geodesic structure for the emergent Barriola–Vilenkin type spacetime

“…Therefore these kind of orbit goes to infinity, asymptotically, along the direction Φ ∞ . In Fig-3 (a), (b) and (c) , the orbits of first kind and second kind are traced with eccentricity e = 3 2 , M = 3 14 , β = 0.3 and various latus rectums l = 15, 17 2 and 14 2 respectively on the basis of the equations (99) and (98) for First kind and equations (68) and (70) for Second kind.…”

“…with eccentricity e = 3 2 , M = 3 14 , β = 0.3 and various latus rectums l = 15, 17 2 and 14 2 respectively on the basis of the equations (99) and (98) for First kind and equations (68) and (70) for Second kind.…”

Gravitational collapse for the K-essence emergent Vaidya spacetime

“…where φ is k-essence scalar field, X = 1 2 g μν ∇ μ φ∇ ν φ and does not depend explicitly on φ to start with [25][26][27][28][29][50][51][52][53][54]. The Lagrangian for k-essence scalar fields contain non-canonical kinetic terms.…”

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 emergent gravity metric Gµν is not conformally equivalent to the gravitational metric g µν . The general form of the lagrangian for k-essence model is: L = −V (φ)F (X) where φ is k-essence scalar field, X = 1 2 g µν ∇ µ φ∇ ν φ and does not depend explicitly on φ to start with [1][2][3][4][5][6][7][8][9][10][11]. The Lagrangian for k-essence scalar fields contain non-canonical kinetic terms.…”