Bach equation and the matching of spacetimes in conformal cyclic cosmology models

Abstract

We consider the problem of matching two spacetimes, the previous and present aeons, in the Conformal Cyclic Cosmology model. The common boundary between them inherits two sets of constraints -- one for each solution of the Einstein field equations extended to the conformal boundaries. The previous aeon is assumed to be an asymptotically de Sitter spacetime, so the standard conformal formulation of the Einstein field equations suffice to derive the constraints on the future null infinity. For the future aeon, which is supposed to evolve from an initial singularity, they are obtained with the use of the Bach equation. This equation is regular at the past conformal infinity for conformally flat and conformally Einstein spacetimes, so we will mostly focus on them here. An example of the electrovacuum spacetime which does not fall into this class and has regular conformal Bach tensor will be discussed in the appendix.

arXiv comment10 pages; updated to match the published version

References in corpus (11)

• Making the Case for Conformal Gravity
• Asymptotics with a positive cosmological constant: I. Basic framework
• Existence and stability of even dimensional asymptotically de Sitter spaces
• Asymptotically simple solutions of the vacuum Einstein equations in even dimensions
• A conformal approach for the analysis of the non-linear stability of pure radiation cosmologies
• Sharp asymptotics for Einstein-$\lambda$-dust flows
• New electromagnetic conservation laws
• A Fundamental Solution to the CCC equation
• Conformal transformations and the beginning of the Universe
• The Chevreton Tensor and Einstein-Maxwell Spacetimes Conformal to Einstein Spaces
• Conformal wave equations for the Einstein-tracefree matter system

Cited by in corpus (1)

• Stress and Geometry for Isotropic Singularities