Fermion tunneling from a Vaidya black hole

Abstract

In this paper, we investigate the fermion tunneling through the event horizon of a Vaidya black hole which is non-stationary. We further take into account the particle's selfgravitation in the dynamical background space-time, and calculate the tunneling probability. The result shows that the tunneling probability is related not only to the change of Bekenstein-Hawking entropy but also to the integral of the changing horizon, which is different from the case of stationary black holes.

Surrounded Vaidya solution by cosmological fields

“…There is a difference in the method obtaining the solutions in the present work and in [50] as well as in the other mentioned works. The solution (20), as in [50], is obtained by the "pre-imposed" equation of state p = kρ a , whereas in our approach, the effective equation of state is resulting from the isotropic averaging over the angles for the surrounding field distribution. Our approach is motivated by the present anisotropy in the Einstein tensor components (2) and the corresponding total energy-momentum tensor (3), such that the surrounding fluid behaves effectively as a perfect fluid with the effective (averaged) equation of state p s (u, r ) = ω s ρ(u, r ), see (7).…”

“…As the advantage of this averaging method, one can substitute for ω s the same known cosmological field equation of state parameters and − 4 3 for the radiation, dust, cosmological, quintessence and phantom fields, respectively, when the black hole is embedded in these cosmological backgrounds. Substituting the same values of cosmological parameters for k, through p = kρ a even for a = 1, in (20) gives different solutions with respect to (17) for the general dynamical case as well as for the known static solution in [51] in the stationary limit, by doing a similar transformation to (18). For example, throwing a bunch of dust with the mass of M dust (= g) to the black hole with mass M, one expects a resulting metric for the final black hole as…”

“…where M e f f = M + M dust , whereas substituting k = 0 in the metric (20) gives f (r ) = 1 − 2M r − 2M dust which seems to be incorrect due to the gravitational potential form of the final black hole and also the dimensional consideration. One also realizes that, as we will see in the next sections of the paper, there is a possibility of the formation of both the naked singularities and black holes in different backgrounds for the solution with = −1.…”

“…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.…”

Higher spins tunneling from a time dependent and spherically symmetric black hole

“…Since k μ k μ = 0, one can consider the Vaidya solution to describe a non-empty spacetime outside of a null radiating mass. Scalar tunneling as a mechanism for Hawking radiation from a Vaidya black hole is also discussed in [68], and the authors of [69,70] Related to the generalized Painlevé transformation (7) and (8), we can take Vaidya black holes [47,71],…”