Cosmology of Schwarzschild de Sitter Black Holes: Exploring Black Holes in an Expanding Universe

In light of recent findings [1], we explore within the framework of General Relativity that an expanding cosmological region could emerge from the interior of a Schwarzschild de Sitter black hole prior to complete gravitational collapse. In this context, we analyze Einstein's field equations and create an explicit analytical model that describes the geometric and causal characteristics of these structures. We study the structure of the resulting singularity and demonstrate that a class of regular internal geometries can be reliably matched at the cosmic horizon to the outside Schwarzschild de Sitter region, which is characterized by a positive cosmological constant. According to our findings, these kinds of arrangements might offer a helpful theoretical framework for investigating the boundaries of classical General Relativity in strong gravitational regimes.