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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.

The k-essence emergent Reissner-Nordstrom-de Sitter spacetime has exactly mapped on to the Robinson-Trautman (RT) type spacetime with cosmological constant Λ for certain configuration of k-essence scalar field. Theoretically, we evaluated that the thermodynamical quantities for the RT type emergent black hole is different from the usual one in the presence of kinetic energy of the k-essence scalar field i.e., the dark energy density. We restrict ourselves into the fact that the dark energy density (K) is to be unity, then the effective temperature and pressure both are negative for the RT type emergent black hole which implies that the system is thermodynamically unstable when the charge Q = 0 and the emergent spacetime is only dark energy dominated and it does not radiate when Q = 0. The thermodynamically unstable situation is physically plausible only when we consider spin degrees of freedom of a system. We have made this analysis in the context of dark energy in an emergent gravity scenario having k-essence scalar fields φ with a Dirac-Born-Infeld type lagrangian. The scalar field also satisfies the emergent equation of motion at r → ∞.

For a particular type of k-essence scalar field, the k-essence emergent gravity metric is exactly mapped on to the Barriola-Vilenkin (BV) type metric for Schwarzschild background established by Gangopadhyay and Manna. Based on the S. Chandrasekhar, we report the exciting features of the time-like geodesic structure in the presence of dark energy in an emergent gravity scenario for this Barriola-Vilenkin type metric. We trace the different kinds of trajectories for time-like geodesic in the presence of dark energy for the k-essence emergent Barriola-Vilenkin spacetime, which are same with the Schwarzchild spacetime in view of the basic orientation, but the allowed ranges of the aphelion and perihelion distances are much more different. The bound and unbound orbits are plotted for a fixed value of the dark energy density. II. REVIEW OF K-ESSENCE THEORY AND EMERGENT GRAVITYIn this section, we present a short review of the kessence theory and construction of the effective emergent metric. The k-essence scalar field φ minimally coupled to the background spacetime metric g µν has action [9]- [13] S k [φ, g µν ] = d 4 x √ −gL(X, φ)

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