Rotating Kinetic Gas Disk Morphology Surrounding a Schwarzschild Black Hole

Abstract

This paper discusses the behavior of a rotating relativistic kinetic gas surrounding a Schwarzschild black hole. We are interested in the description and analysis of the morphology of the resulting configurations for kinetic gas clouds with and without total angular momentum, and we also compare the macroscopic observables with configurations of finite total mass. Considering models for the one-particle distribution function based on a polytropic ansatz and the inclination angle of the orbits of the particles in the kinetic gas, a collisionless gas in the Schwarzschild spacetime background is analyzed. Profiles of the macroscopic observables of the gas configurations are presented, which are derived from the density current vector field and energy-momentum-stress tensor.

Figures (22)

• Figure 1: Behavior of the effective potential $V_{m,L}$ as a function of the radial coordinate $r$ for different values of $L$.
• Figure 2: Effective potential $V_{m,L}(r)$ for $L=\sqrt{20}Mm$. The purple shaded area represents the trajectories of particles absorbed by the black hole. The yellow shaded area corresponds to the trajectories of particles that are scattered by the potential barrier. Finally, the green shaded area corresponds to particles whose trajectories are bounded.
• Figure 3: Log-log plot showing the behavior of the particle density normalized by $\mathcal{N}_{\textrm{gas}}$ as a function of the dimensionless areal radius $\xi$ in the equatorial plane for an asymptotically infinite extended non-rotating configuration of gas. Left panel: plot for different parameter values of $k=6,7,8$ and $(s,\varepsilon_0)=(1,1)$. Right panel: plot for different parameter values of $s=1,2,3$ and $(k,\varepsilon_0)=(6,1)$.
• Figure 4: Log-log plot showing the behavior of the particle density normalized by $\mathcal{N}_{\textrm{gas}}$ as a function of the dimensionless areal radius $\xi$ in the equatorial plane for a finite extended non-rotating configuration of gas. Left panel: plot for different parameter values of $k=6,7,8$ and $(s,\varepsilon_0)=(1,0.98)$. Right panel: plot for different parameter values of $s=1,2,3$ and $(k,\varepsilon_0)=(6,0.98)$. The dotted vertical lines represent the radial coordinates where the configuration drops to zero.
• Figure 5: Contour plots of the particle density normalized by $\mathcal{N}_{\textrm{gas}}$ for a fixed value of $k$ and different values of $s$ in a non-rotating kinetic gas configuration of asymptotically infinite extension. Left panel: plot for different parameter values of $(k,s,\varepsilon_0)=(6,1,1)$. Right panel: plot for different parameter values of $(k,s,\varepsilon_0)=(6,2,1)$.