超引力和其它理论对黑洞中光子球和声波视界的研究
Photon Spheres and Sonic Horizons in Black Holes from Supergravity and Other Theories
摘要：
我们研究了超引力理论、Horndeski理论和精粹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），这些轨道就位于我们称之为光子球（反光子球）的地方。我们证明了在所有的渐近平坦的解决方案，我们检查，承认一个规则的事件视界，其能量动量张量满足强能量条件，有一个且只有一个光子球外的事件视界。我们给出一个Horndeski理论的例子黑洞（其能量动量张量违反强能量条件），其度规允许一个光子球和一个反光子球。在规范超引力中，渐近反de Sitter解的唯一性和不存在性也成立。后者也表现出投影对称性，这是首次发现的施瓦茨希尔德-德西特度规：非参数化的零测地线是相同的，当宇宙或规范耦合常数为零。我们还研究了密切相关的问题吸积流动的完美流体在这些指标。对于辐射流体，邦迪的声波视界与光子球重合。对于一般的多方状态方程，情况并非如此。最后，我们展示了一个猜想的Hod的反例。
英文摘要：
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.
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