Hawking radiation as tunneling from a Vaidya black hole in noncommutative gravity

Abstract

In the context of a noncommutative model of coordinate coherent states, we present a Schwarzschild-like metric for a Vaidya solution instead of the standard Eddington-Finkelstein metric. This leads to the appearance of an exact (t − r) dependent case of the metric. We analyze the resulting metric in three possible causal structures. In this setup, we find a zero remnant mass in the long-time limit, i.e. an instable black hole remnant. We also study the tunneling process across the quantum horizon of such a Vaidya black hole. The tunneling probability including the time-dependent part is obtained by using the tunneling method proposed by Parikh and Wilczek in terms of the noncommutative parameter σ. After that, we calculate the entropy associated to this noncommutative black hole solution. However the corrections are fundamentally trifling; one could respect this as a consequence of quantum inspection at the level of semiclassical quantum gravity.

Charged Particle’s Tunneling in a Modified Reissner-Nordstrom Black Hole

“…Then, from (43) and (47), it is implied that, information conservation of black hole is still possible when the quantum corrections of black hole entropy are considered. In addition, the corrected item S QC of the black hole entropy can be calculated by giving the specific form of the energy function f [39,40,62,68].…”

“…Thence, by the Hamilton-Jacobi method, the quantum correction to the tunneling program was discussed and the quantum corrected entropy of black holes was calculated [26][27][28][29][30][31][32][33]. Also, in the radial trajectory method, the quantum effects of spacetime was considered and the emission rate was related the quantum corrected entropy of black hole [34][35][36][37][38][39][40][41][42][43]. These results show that, considering the quantum corrections of black hole entropy and spacetime, information conservation of black hole is still possible.…”

Surrounded Vaidya solution by cosmological fields

“…Then, the evaporating black hole in an empty background, i.e ρ s = 0 [8,9], and (anti)-de Sitter space, i.e ρ s = ρ = constant [45,109,110], are special subclasses of our general solution. Some interesting physical features of these solutions can be found in the references [11,12,31,42,[111][112][113][114][115][116][117][118][119].…”

“…Afterwards, some models to describe the classical essence of this radiation in a language which is free from the usual quantum field theoretic tools and is more familiar to the astrophysicists and relativists, have been introduced. For instance, the Vaidya solution [8][9][10] has provided a simple classical model for the black hole radiation and has been vastly investigated in this regard [11][12][13][14][15][16][17], see also [18][19][20][21][22][23][24][25][26][27][28][29] for more studies. In fact, the Vaidya solution is one of the non-static solutions of the Einstein field equations and can be regarded as a generalization of the static Schwarzschild black hole solution.…”

Hawking non-thermal and thermal radiations of Schwarzschild anti-de Sitter black hole by Hamilton-Jacobi method

“…Both the methods show that when the self-gravitational interaction and the unfixed background spacetime are taken into account, the actual Hawking radiation spectrum deviates from the purely thermal one, satisfies the underlying unitary theory and gives a leading correction to the radiation spectrum. Extending these methods to general case, a lot of works for various spacetimes have been done [16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41] and all of these are limited to massless particle.…”