Scattering and absorption sections of Schwarzschild-anti de Sitter with quintessence

In this paper, we study the scattering and absorption sections of the Schwarzschild--anti de Sitter black hole surrounded by quintessence. The critical values of the cosmological constant and the normalization factor are obtained. We describe the event horizons and the extremal condition of the black hole surrounded by quintessence. The effects of quintessence on the classical and semi--classical scattering cross--sections have been estimated. Also, the absorption section is studied with the sinc approximation in the eikonal limit. We consider the quintessence state parameter in the particular cases ω = -2/3 and ω = -1/2.

Connection between Sinc Approximation for High-Energy Absorption Cross Section and Shadow of Black Holes

This letter aims to show the connection between the sinc approximation for high-energy absorption cross section and the shadow radius of the spherically symmetric black hole. This connection can give a physical interpretation of the absorption cross section in the eikonal limit parameters. Moreover, the use of this alternative way, one can extract its shadow radius from the absorption cross section in high energy limits to gain more information about the black hole spacetime. Our results indicate that the increasing the value of the shadow radius of the black hole, exponentially increase the the absorption cross section of the black hole in high-energy limits which can be captured by the Event Horizon Telescope (EHT) collaboration.

Design of accurate formulas for approximating functions in weighted Hardy spaces by discrete energy minimization

We propose a simple and effective method for designing approximation formulas for weighted analytic functions. We consider spaces of such functions according to weight functions expressing the decay properties of the functions. Then we adopt the minimum worst error of the $n$-point approximation formulas in each space for characterizing the optimal sampling points for the approximation. In order to obtain approximately optimal sampling points we consider minimization of a discrete energy related to the minimum worst error. Consequently, we obtain an approximation formula and its theoretical error estimate in each space. In addition, from some numerical experiments, we observe that the formula generated by the proposed method outperforms the corresponding formula derived with sinc approximation, which is near optimal in each space.