Cosmological Black hole Candidates: A Detailed Analysis of McVittie, Culetu, Sultana-Dyer, and Glass-Mashhoon Spacetimes

Abstract: This paper investigates the existence of cosmological black holes by analyzing the properties of trapping horizons in detail, based on Hayward's formalism of future outer and past inner trapping horizons, in several dynamical spacetimes embedded in an expanding universe. Through a detailed examination of the McVittie, Culetu, and Sultana--Dyer metrics, as well as the generalized Glass--Mashhoon solution, we evaluate the existence and characteristics of trapping horizons and energy conditions. The Glass--Mashhoon solution provides an analytical model for spherical stellar collapse. However, it is shown that, as long as certain conditions are satisfied, it lacks suitable future outer trapping horizons, meaning it does not represent a cosmological black hole. As a result, the McVittie class of solutions also fails to describe a cosmological black hole. Conversely, the Culetu and Sultana--Dyer spacetimes can describe a cosmological black hole in the matter-dominated early universe, provided that the relevant energy conditions are satisfied.