Title: Photon Spheres and Sonic Horizons in Black Holes from Supergravity and Other Theories Show Chinese title

Title: 光球面和黑洞中的声视界来自超引力和其他理论

Abstract: We study closed photon orbits in spherically-symmetric static solutions of supergravity theories, a Horndeski theory, and a theory of quintessence. These orbits lie in what we shall call a photon sphere (anti-photon sphere) if the orbit is unstable (stable). We show that in all the asymptotically flat solutions we examine that admit a regular event horizon, and whose energy-momentum tensor satisfies the strong energy condition, there is one and only one photon sphere outside the event horizon. We give an example of a Horndeski theory black hole (whose energy-momentum tensor violates the strong energy condition) whose metric admits both a photon sphere and an anti-photon sphere. The uniqueness and non-existence also holds for asymptotically anti-de Sitter solutions in gauged supergravity. The latter also exhibit the projective symmetry that was first discovered for the Schwarzschild-de Sitter metrics: the unparameterised null geodesics are the same as when the cosmological or gauge coupling constant vanishes. We also study the closely related problem of accretion flows by perfect fluids in these metrics. For a radiation fluid, Bondi's sonic horizon coincides with the photon sphere. For a general polytropic equation of state this is not the case. Finally we exhibit counterexamples to a conjecture of Hod's. Show Chinese abstract

Abstract: 我们研究了超引力理论、霍尔德斯基本构理论以及 quintessence 理论的球对称静态解中的闭合光子轨道。如果轨道是不稳定的（稳定的），这些轨道位于我们称之为光子球（反光子球）的区域。我们证明，在所有我们考察的渐近平坦解中，若它们具有正则事件视界且能量-动量张量满足强能量条件，则在外侧事件视界外存在唯一一个光子球。我们给出一个例子：霍尔德斯基本构理论黑洞（其能量-动量张量违反强能量条件），其度规同时允许光子球和反光子球的存在。这种唯一性和不存在性同样适用于规范超引力中的渐近反德西特解。后者也表现出首次在施瓦西-德西特度规中发现的投影对称性：未参数化的零测地线与宇宙学常数或规范耦合常数为零时相同。我们还研究了这些度规中完美流体吸积流的密切相关问题。对于辐射流体，邦迪声学视界与光子球重合。但对于一般的多态方程状态则不然。最后，我们给出了霍德猜想的一些反例。