Matching radiation-dominated and matter-dominated Einstein–de Sitter universes and an application for primordial black holes in evolving cosmological backgrounds

Abstract

By matching across a surface of constant time, it is demonstrated that the spacetime for a radiation-dominated Einstein-de Sitter universe can be directly matched to the spacetime for a matter-dominated Einstein-de Sitter universe. Thus, this can serve as a model of a universe filled with radiation that suddenly is converted to matter and antimatter, or a universe filled with matter and antimatter that suddenly annihilates to leave radiation. This matching is shown to hold for asymptotically Einstein-de Sitter cosmological black hole spacetimes, yielding simplistic models of primordial black holes that evolve between being in radiation-dominated universes and matter-dominated universes.

Cosmological and Black Hole Apparent Horizons

“…3P/ [58,117,118,[130][131][132]161], violating the weak and null energy conditions (but not the positivity of the energy density) in a neighbourhood of the singularity. The de Sitter "background" is an exception: in this case it is P H D 0 identically and the second term on the right hand side of Eq.…”

“…This technique generates, for example, the Sultana-Dyer black hole and various solutions studied in[116][117][118]. 2.…”

Embedding Black Holes and Other Inhomogeneities in the Universe in Various Theories of Gravity: A Short Review

“…Many do not have reasonable matter sources and the energy density becomes negative in certain spacetime regions. Often these solutions are obtained by conformally transforming a stationary black hole solution or by performing a Kerr-Schild transformation of a stationary black hole metric g ab , g ab →ḡ ab = g ab + λk a k b , (3.117) where λ is a function of the spacetime position and the vector k a is null and geodesic with respect to both g ab andḡ ab [78,79,89,90,91,92].…”

Inhomogeneities in Cosmological “Backgrounds” in Einstein Theory

“…3P/ [58,117,118,[130][131][132]161], violating the weak and null energy conditions (but not the positivity of the energy density) in a neighbourhood of the singularity. The de Sitter "background" is an exception: in this case it is P H D 0 identically and the second term on the right hand side of Eq.…”