Singular hypersurfaces and thin shells in cosmology

Abstract

We analyse spherically symmetric spacetimes obtained by gluing a cosmological region to a Schwarzschild black hole across a singular co-dimension one hypersurface. Assuming an arbitrary homogeneous and isotropic cosmology, and working in spacetime dimensions greater than three with general cosmological constant, we derive the stress-energy tensor required on the hypersurface directly in terms of the cosmological energy density. This general framework yields a new exact solution in four dimensions describing a radiation-filled cosmology matched to vacuum through a pressureless dust shell. A systematic exploration of parameter space reveals twenty-two distinct families of solutions, including bubble-of-cosmology and Swiss-cheese spacetimes with different global and causal structures. We also discuss possible generalisations of the construction and explain why such thin-shell cosmologies are of interest in the context of holography and quantum cosmology. For negative cosmological constant, a subset of these solutions admits a Euclidean continuation compatible with a holographic interpretation developed in related work. In addition, we provide a pedagogical introduction to hypersurfaces in general relativity and a practical framework for constructing thin-shell spacetimes.

31 pages, 32 figures, 1 table. Updated version contains a new section on generalisations and applications, and expanded discussions. Phys. Scr (2026)