Photon Rings and Mass-Independent Observables of a Five-Dimensional Charged AdS Black Hole

Abstract

We investigate the optical properties of a five-dimensional charged anti-de Sitter (AdS) black hole. Using the null geodesic equations, we determine the event horizon and photon sphere radii and the critical impact parameter, showing that all decrease with increasing charge, while the photon sphere radius remains independent of the AdS radius. To avoid dependence on the mass scale and the observer-dependent apparent size of the shadow in an AdS spacetime, we introduce two mass-independent geometric observables: the subring exponent $γ$ and the ratio of the critical impact parameter to that of the direct image of the innermost stable circular orbit (ISCO). We derive $γ$ in closed form and show that it is independent of the AdS radius and satisfies $2π/\sqrt{3}<γ\leqπ\sqrt{2}$, above the values for four-dimensional Schwarzschild and Reissner--Nordström black holes. Using a Markov chain Monte Carlo (MCMC) forecast based on noiseless mock data with illustrative fractional uncertainties of $5\%$, we find that the dimensionless AdS radius can be constrained with a relative uncertainty of $16$--$19\%$, whereas the charge can be distinguished from zero only for the near-extremal fiducial model considered. Under these assumptions, the subring exponent provides a Gaussian separation of $3.4$--$5.9σ$ from the four-dimensional Schwarzschild black hole.