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

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