Abstract
It is well known that quantum effects may lead to removal of the intrinsic singularity point of back holes. Also, the quintessence scalar field is a candidate model for describing late-time acceleration expansion. Accordingly, Kazakov and Solodukhin considered the existence of back-reaction of the spacetime due to the quantum fluctuations of the background metric to deform a Schwarzschild black hole, which led to a change of the intrinsic singularity of the black hole to a 2-sphere with a radius of the order of the Planck length. Also, Kiselev rewrote the Schwarzschild metric by taking into account the quintessence field in the background. In this study, we consider the quantum-corrected Schwarzschild black hole inspired by Kazakov–Solodukhin’s work, and the Schwarzschild black hole surrounded by quintessence deduced by Kiselev to study the mutual effects of quantum fluctuations and quintessence on the accretion onto the black hole. Consequently, the radial component of the 4-velocity and the proper energy density of the accreting fluid have a finite value on the surface of its central 2-sphere due to the presence of quantum corrections. Also, by comparing the accretion parameters in different kinds of black holes, we infer that the presence of a point-like electric charge in the spacetime is somewhat similar to some quantum fluctuations in the background metric.
Highlights
Introduction to KS black holeFollowing Ref. [7], it is possible to change the central point-like singularity of the SCH black hole to a central 2dimensional spherical region with radius a which is of the order of the Planck length r ∼ lPl ≡ a to obtain the KS black hole
The presence of the quantum fluctuations in the KS, the IKSK, and the RNKSK black holes leads to a finite, physical large value for the proper energy density, which means that the accreting matter spreads and moves around the central 2-sphere, rather than falling into a point-like singularity
We have considered accretion onto the quantumcorrected Schwarzschild black hole (KS black hole), and this quantum-corrected black hole surrounded by the quintessence field (KSK black hole)
Summary
Following Ref. [7], it is possible to change the central point-like singularity of the SCH black hole to a central 2dimensional spherical region with radius a which is of the order of the Planck length r ∼ lPl ≡ a to obtain the KS black hole. [7]), the line element of the KS black hole can be found as follows: ds2 = f (r ) dt2 − dr 2 − r 2 dθ 2 + sin θ dφ2 ,. In order to find the horizons of the KS black hole, one is required to compute the roots of f (r ) in Eq (3), i.e., f (r ) = 0 , which are as follows: r±. Heading from the outside of the event horizon to the region between two horizons, the behavior of the t-coordinate (r coordinate), will change from time-like (space-like) to spacelike (time-like). Crossing from the region between two horizons to the central 2-sphere with radius a, the behavior of the t-coordinate (r -coordinate) will change from spacelike (time-like) to time-like (space-like). In the KS black hole, r− is the inner/Cauchy horizon, and r+ is the event horizon, completely similar to the RN black hole
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