论文标题
声点和光子表面
Sonic Point and Photon Surface
论文作者
论文摘要
在一般环境中对声点/光子表面对应关系进行彻底研究。首先，我们研究了一般固定时空中跨音速稳定完美流体流的声点，尤其是针对辐射流体。流量必须在声音点上满足的必要条件是作为流体力学中流线的一致性运动量的条件。我们将声音点的条件与光子表面的概念进行了比较，该概念可以定义为完全脐带超出表面。结果，我们发现，为了实现声点/光子表面对应关系，必须由$ 1/\ sqrt {d} $给出声音$ v _ {\ rm s} $的速度，其中$ d $是SPACETIME的空间维度。对于辐射流体（$ v _ {\ rm s} = 1/\ sqrt {d} $），我们确认条件的一部分由声音点和光子表面共享。但是，通常，一组声音点的邦迪表面不一定与光子表面一致。其他假设（例如空间对称性）对于在所有已知示例中实现声点/光子表面对应关系至关重要。
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.
