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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.
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In an accretion of fluid, its velocity may transit from subsonic to supersonic. The point at which such transition occurs is called sonic point and often mathematically special. We consider a steady-state and spherically symmetric accretion problem of ideal photon gas in general static spherically symmetric spacetime neglecting back reaction. Our main result is that the EOS of ideal photon gas leads to correspondence between its sonic point and the photon sphere of the spacetime in general situations. Despite of the dependence of the EOS on the dimension of spacetime, this correspondence holds for spacetimes of arbitrary dimensions.
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, Bondis 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 Hods.
We study the Bondi-Sachs rockets with nonzero cosmological constant. We observe that the acceleration of the systems arises naturally in the asymptotic symmetries of (anti-) de Sitter spacetimes. Assuming the validity of the concepts of energy and mass previously introduced in asymptotically flat spacetimes, we find that the emission of pure radiation energy balances the loss of the Bondi mass in certain special families of the Bondi-Sachs rockets, so in these there is no gravitational radiation.
We study the properties of the loosely trapped surface (LTS) and the dynamically transversely trapping surface (DTTS) in Einstein-Maxwell systems. These concepts of surfaces were proposed by the four of the present authors in order to characterize strong gravity regions. We prove the Penrose-like inequalities for the area of LTSs/DTTSs. Interestingly, although the naively expected upper bound for the area is that of the photon sphere of a Reissner-Nordstroem black hole with the same mass and charge, the obtained inequalities include corrections represented by the energy density or pressure/tension of electromagnetic fields. Due to this correction, the Penrose-like inequality for the area of LTSs is tighter than the naively expected one. We also evaluate the correction term numerically in the Majumdar-Papapetrou two-black-hole spacetimes.
In the presence of a black hole, light sources connect to observers along multiple paths. As a result, observed brightness fluctuations must be correlated across different times and positions in black hole images. Photons that execute multiple orbits around the black hole appear near a critical curve in the observer sky, giving rise to the photon ring. In this paper, a novel observable is proposed: the two-point correlation function of intensity fluctuations on the photon ring. This correlation function is analytically computed for a Kerr black hole surrounded by stochastic equatorial emission, with source statistics motivated by simulations of a turbulent accretion flow. It is shown that this two-point function exhibits a universal, self-similar structure consisting of multiple peaks of identical shape: while the profile of each peak encodes statistical properties of fluctuations in the source, the locations and heights of the peaks are determined purely by the black hole parameters. Measuring these peaks would demonstrate the existence of the photon ring without resolving its thickness, and would provide estimates of black hole mass and spin. With regular monitoring over sufficiently long timescales, this measurement could be possible via interferometric imaging with modest improvements to the Event Horizon Telescope.
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