# Photon surfaces in spherically, planar and hyperbolically symmetric spacetimes of D-dimensions: Sonic point/photon sphere correspondence

## TL;DR

This paper extends the sonic point/photon sphere correspondence to spherically, planarly, and hyperbolically symmetric spacetimes of arbitrary dimensions, establishing a link between fluid flow sonic points and photon surfaces.

## Contribution

It generalizes the SP/PS correspondence to non-spherical symmetries and different spacetime geometries, proving the existence of the correspondence in these broader contexts.

## Key findings

- Sonic points are always on photon surfaces in non-spherical symmetric spacetimes.
- The correspondence holds for radial fluid flows in various symmetric spacetimes.
- Photon surfaces serve as the non-spherical analogue of photon spheres.

## Abstract

Sonic point/photon sphere (SP/PS) correspondence is a theoretical phenomenon which appears in fluid dynamics on curved spacetime and its existence has been recently proved in quite wide situations as theorems. The theorems state that a sonic point (SP) of radiation fluid flow must be on an unstable photon sphere (PS) when the fluid flows radially or rotationally on an equatorial plane in spherically symmetric spacetime of arbitrary dimensions. In this paper, we investigate SP/PS correspondence in spherically, planarly and hyperbolically symmetric spacetime. As the corresponding objects of photon spheres in non-spherically symmetric spacetime, we consider photon surfaces introduced by Claudel {\it et al.} (2001) in the spacetime. After formulating the problem of radial fluid flows, we prove there always exists a correspondence between the sonic points and the photon surfaces, namely, SP/PS correspondence in non-spherically symmetric spacetime.