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.

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 θ = 0, the emergent black hole metric satisfies Einstein's equations for large r and always radiates. Our analysis is done in the context of emergent gravity metrics having k-essence scalar fields φ with a Born-Infeld type lagrangian. In both cases the scalar field φ(r, t) = φ 1 (r )+φ 2 (t) also satisfies the emergent gravity equations of motion for r → ∞ and θ = 0.

In this paper, we study the gravitational collapse in the k-essence emergent gravity using a generalized Vaidya-type metric as a background. We also analyze the cosmic censorship hypothesis for this system. We show that the emergent gravity metric resembles closely to the new type of the generalized Vaidya metrics for null fluid collapse with the k-essence emergent mass function, where we consider the k-essence scalar field being a function solely of the advanced or the retarded time. This new type of k-essence emergent Vaidya metric has satisfied the required energy conditions. The existence of the locally naked central singularity, the strength and the strongness of the singularities for the kessence emergent Vaidya metric are the interesting outcomes of the present work.

No 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.