Potential flows in the Reissner-Nordstr\"om-(anti) de Sitter metric: numerical results

TL;DR

This paper presents numerical solutions for steady-state ideal fluid flows around black holes and spheres in Reissner-Nordström-(anti) de Sitter spacetimes, analyzing streamlines, density contours, and accretion rates.

Contribution

It provides detailed numerical analysis of fluid dynamics in complex spacetime geometries, highlighting effects of electric charge and cosmological constant on flow properties.

Findings

Fluid properties are more sensitive to charge and cosmological constant for γ ≠ 2.

Accretion rate varies with the cosmological constant, increasing or decreasing accordingly.

Density contours reveal detailed flow structures around black holes and spheres.

Abstract

Numerical solutions for the integral curves of the velocity field (streamlines), the density contours, and the accretion rate of a steady-state flow of an ideal fluid with $p=K n^\gamma$ equation of state are presented. The streamlines and velocity fields associated with a black hole and a rigid sphere in a Reissner-Nordstr\"om-(anti) de Sitter spacetimes are studied in some detail. For each case the fluid density is studied using contour lines. For $\gamma \neq 2$, we found that the studied properties of the fluid are more sensitive to variations of the electric charge and the cosmological constant. Also, the accretion rate was found to increase or decrease when the cosmological constant increases or decreases respectively.