The sonic point/photon surface correspondence is thoroughly investigated in a general setting. First, we investigate a sonic point of a transonic steady perfect fluid flow in a general stationary spacetime, particularly focusing on the radiation fluid. The necessary conditions that the flow must satisfy at a sonic point are derived as conditions for the kinematical quantities of the congruence of streamlines in analogy with the de Laval nozzle equation in fluid mechanics. We compare the conditions for a sonic point with the notion of a photon surface, which can be defined as a timelike totally umbilical hypersurface. As a result, we find that, for the realization of the sonic point/photon surface correspondence, the speed of sound $v_{\rm s}$ must be given by $1/\sqrt{d}$ with $d$ being the spatial dimension of the spacetime. For the radiation fluid ($v_{\rm s}=1/\sqrt{d}$), we confirm that a part of the conditions is shared by the sonic point and the photon surface. However, in general, a Bondi surface, a set of sonic points, does not necessarily coincide with a photon surface. Additional assumptions, such as a spatial symmetry, are essential to the realization of the sonic point/photon surface correspondence in all known examples.
Photon surfaces in spherically, planar and hyperbolically symmetric spacetimes of D-dimensions: Sonic point/photon sphere correspondence
声波点/光子球（SP/PS）对应是弯曲时空上流体动力学中的一种理论现象，它的存在性近年来已在相当广泛的情况下被证明为定理。这些定理指出，当流体在任意维度的球对称时空中在赤道平面上径向或旋转流动时，辐射流体流的声点（SP）必须位于不稳定的光子球（PS）上。本文研究了球对称、平面对称和双曲对称时空中的SP/PS对应。作为非球对称时空中光子球的对应对象，我们考虑了Claudel { \it et al.}（2001）在时空中。在建立了径向流体流动问题之后，我们证明了在非球对称时空中，声波点和光子面之间总是存在一种对应，即SP/PS对应。
Photon surfaces extensions for dynamical gravitational collapse
School of Science and Technology, Mathematics Division, Università di Camerino（卡梅里诺大学理学院数学系）；Osservatorio Astronomico di Brera, INAF（布雷拉天文台，意大利国家天体物理研究所）
光子曲面是洛伦兹时空的类时、全脐超曲面。在本文的第一部分中，我们局部地刻画了一类静态球对称时空中所有可能的光子表面，包括Schwarzschild，Reissner-Nordström，Schwarzschild-anti de Sitter等，在$n+1$维度上。在第二部分中，我们证明了任何静态的，真空的，“渐近各向同性”的$n+1$维时空，拥有我们所说的“等势”和“向外指向”的光子表面是等距的史瓦西时空相同的（必然是正的）质量，使用的唯一性结果由第一命名的作者。
