Horizons

In this chapter we assemble the problems that concern one of the most distinctive features of General Relativity and Cosmology - the horizons. The first part gives an elementary introduction into the concept in the cosmological context, following and borrowing heavily from the most comprehensible text by E. Harrison ^[1]. Then we move to more formal exposition of the subject, making use of the seminal works of W. Rindler^[2] and G.F.R. Ellis, T. Rothman^[3], and consider first simple, and then composite models, such as $\Lambda$CDM. The fourth section elevates the rigor one more step and explores the causal structure of different simple cosmological models in terms of conformal diagrams, following mostly the efficient approach of V. Mukhanov^[4], and inflation. The section on black holes relates the general scheme of constructing conformal diagrams for stationary black hole spacetimes, following mostly the excellent textbook of K. Bronnikov and S. Rubin^[5]. The consequent sections focus on more specific topics, such as the various problems regarding the Hubble sphere, inflation and holography.