Flat from anti-de Sitter

TL;DR

This paper derives Ricci-flat solutions in four dimensions as limits of anti-de Sitter spacetimes, revealing boundary data structures and flux-balance laws through a covariant approach involving Carrollian geometry.

Contribution

It introduces a novel method to obtain flat spacetime solutions from AdS by expanding the energy-momentum tensor and analyzing boundary structures using Carrollian geometry.

Findings

Ricci-flat solutions as AdS limits

Boundary data characterized by Laurent series expansion

Flux-balance equations derived from boundary conditions

Abstract

Ricci-flat solutions to Einstein's equations in four dimensions are obtained as the flat limit of Einstein spacetimes with negative cosmological constant. In the limiting process, the anti-de Sitter energy--momentum tensor is expanded in Laurent series in powers of the cosmological constant, endowing the system with the infinite number of boundary data, characteristic of the asymptotically flat solution space. The governing flat Einstein dynamics is recovered as the limit of the original energy--momentum conservation law and from the additional requirement of the line-element finiteness, providing at each order the necessary set of flux-balance equations for the boundary data. This analysis is conducted using a covariant version of the Newman--Unti gauge designed for taking advantage of the boundary Carrollian structure emerging at vanishing cosmological constant and its Carrollian attributes such as the Cotton tensor.