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Abstract: The space of solutions of Einstein's equations is severely altered by the presence of a cosmological constant. This is manifest when solving the equations of motion close to the boundary of spacetime. In AdS all information about the solutions in encoded a metric and an energy-momentum tensor defined on the time-like boundary. On the other hand, at null infinity the information about the solutions is encoded in an infinite number of functions, satisfying suitable flux-balance laws. In spite of these striking differences, we show how the space of Ricci-flat manifolds can be recovered from that of Einstein spaces by expanding the AdS boundary energy-momentum in powers of the cosmological constant. In this process, the flux-balance laws are also recovered by demanding that the line element remains finite in the limit of vanishing cosmological constant. The analysis is performed in a modified version of the Newman-Unti gauge, that has the additional advantage of naturally disclosing the Carrollian structures emerging at null infinity.
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Tringas, Georgios
