Rotating accretion flows in $D$ dimensions: sonic points, critical points and photon spheres

TL;DR

This paper analyzes rotating accretion flows in D-dimensional spacetimes, establishing conditions for sonic and critical points, and demonstrating that for ideal photon gas, sonic points coincide with unstable photon spheres, extending previous spherical flow results.

Contribution

It introduces a model for rotating accretion flows in D-dimensional spacetimes and proves the correspondence between sonic points and photon spheres for ideal photon gas.

Findings

Critical points are explicitly classified and coincide with sonic points.

For ideal photon gas, sonic points always lie on unstable photon spheres.

The analysis extends the spherical flow correspondence to rotating accretion disks.

Abstract

We give the formulation and the general analysis of the rotational accretion problem on $D$-dimensional spherical spacetime and investigate sonic points and critical points. First, we construct the simple two-dimensional rotating accretion flow model in general $D$-dimensional static spherically symmetric spacetime and formulate the problem. The flow forms a two-dimensional disk lying on the equatorial plane and the disk is assumed to be geometrically thin and has uniform distribution in the polar angle directions. Analyzing the critical point of the problem, we give the conditions for the critical point and its classification explicitly and show the coincidence with the sonic point for generic equation of state (EOS). Next, adopting the EOS of ideal photon gas to the analysis, we reveal that there always exists a correspondence between the sonic points and the photon spheres of the spacetime. Our main result is that the sonic point of the rotating accretion flow of ideal photon gas must be on (one of) the unstable photon sphere(s) of the spacetime in arbitrary spacetime dimensions. This paper extends this correspondence for spherical flows shown in the authors' previous work to rotating accretion disks.