Stable photon orbits in stationary axisymmetric spacetimes with an electromagnetic field and a cosmological constant

Stable light rings, which are associated with spacetime instabilities, are known to exist in four-dimensional stationary axisymmetric spacetimes that solve the Einstein\unicode{x2013}Maxwell equations (so-called electrovacuum solutions, with Faraday tensor $F_{\mu \nu} \neq 0$); however, they are not permitted in pure vacuum ($F_{\mu \nu} = 0$). In this work, we extend this result to spacetimes with a non-zero cosmological constant $\Lambda$. In particular, we demonstrate that stable light rings are permitted in $\Lambda$-electrovacuum ($F_{\mu \nu} \neq 0$, $\Lambda \neq 0$), but ruled out in $\Lambda$-vacuum ($F_{\mu \nu} = 0$, $\Lambda \neq 0$).Comment: 6 pages, 1 figur

Stable photon orbits in stationary axisymmetric electrovacuum spacetimes

We investigate the existence and phenomenology of stable photon orbits (SPOs) in stationary axisymmetric electrovacuum spacetimes in four dimensions. First, we review the classification of equatorial circular photon orbits on Kerr-Newman spacetimes in the charge-spin plane. Second, using a Hamiltonian formulation, we show that Reissner-Nordström diholes (a family encompassing the Majumdar-Papapetrou and Weyl-Bach special cases) admit SPOs, in a certain parameter regime that we investigate. Third, we explore the transition from order to chaos for typical SPOs bounded within a toroidal region around a dihole, via a selection of Poincaré sections. Finally, for general axisymmetric stationary spacetimes, we show that the Einstein-Maxwell field equations allow for the existence of SPOs in electro vacuum, but not in pure vacuum

Binary black hole shadows, chaotic scattering and the Cantor set

We investigate the qualitative features of binary black hole shadows using the model of two extremally charged black holes in static equilibrium (a Majumdar–Papapetrou solution). Our perspective is that binary spacetimes are natural exemplars of chaotic scattering, because they admit more than one fundamental null orbit, and thus an uncountably infinite set of perpetual null orbits which generate scattering singularities in initial data. Inspired by the three-disc model, we develop an appropriate symbolic dynamics to describe planar null geodesics on the double black hole spacetime. We show that a one-dimensional (1D) black hole shadow may constructed through an iterative procedure akin to the construction of the Cantor set; thus the 1D shadow is self-similar. Next, we study non-planar rays, to understand how angular momentum affects the existence and properties of the fundamental null orbits. Taking slices through 2D shadows, we observe three types of 1D shadow: regular, Cantor-like, and highly chaotic. The switch from Cantor-like to regular occurs where outer fundamental orbits are forbidden by angular momentum. The highly chaotic part is associated with an unexpected feature: stable and bounded null orbits, which exist around two black holes of equal mass M separated by a1 < a < √ 2a1, where a1 = 4M/√ 27. To show how this possibility arises, we define a certain potential function and classify its stationary points. We conjecture that the highly chaotic parts of the 2D shadow possess the Wada property. Finally, we consider the possibility of following null geodesics through event horizons, and chaos in the maximally extended spacetime