Cosmological black hole shadows

Abstract

A black hole (BH) shadow is a dark region on an observer鈥檚 sky where light from distant sources is completely absorbed due to a BH鈥檚 strong gravitational pull. The first direct image of a BH shadow, captured by the Event Horizon Telescope (EHT) in 2019, not only confirmed the existence of BHs, but also highlighted the importance of understanding their visual appearance. The angular size of a BH鈥檚 shadow is significantly larger than its event horizon, since the former is determined by the gravitational lensing of light rays emitted from unstable photon orbits. This dissertation presents an in-depth theoretical study of BH shadows across various spacetimes, with a focus on the impact of cosmic expansion. We begin by analysing static and spherically symmetric BH spacetimes, deriving a general expression for their shadow鈥檚 angular size and applying it to the Schwarzschild and Reissner-Nordstr枚m solutions. Next, we explore stationary spacetimes, where inertial frame-dragging effects in rotating BHs deform the shadow shape. In particular, the photon orbits and the BH shadow in the Kerr spacetime were studied extensively. Finally, we investigate cosmological BHs embedded in an expanding FLRW universe, using the Kottler (Schwarzschild-de Sitter) and McVittie solutions to model how a dynamic universe influences shadows for both static and comoving observers. This leads us to develop an approach for obtaining the angular size of a BH shadow in a general cosmology.