Flat from anti-de Sitter

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.

1+47 pages

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Cited by in corpus (15)

• The partial Bondi gauge: Gauge fixings and asymptotic charges
• Celestial $w_{1+\infty }$ charges and the subleading structure of asymptotically-flat spacetimes
• Carroll Hawking effect
• Chern-Simons action and the Carrollian Cotton tensors
• Radiation in Fluid/Gravity and the Flat Limit
• Quantization of Carrollian fermions
• A Carroll Limit of AdS/CFT: A Triality with Flat Space Holography?
• Supersymmetric Carroll Galileons in Three Dimensions
• Celestial $s{w}_{1+\infty }$ algebra in Einstein-Yang-Mills theory
• Carroll-Schrödinger Equation
• One-dimensional Carrollian fluids I: Carroll-Galilei duality
• Finite actions and asymptotic charges at null infinity for any spin
• Flat Holography & Holographic Renormalization: Scalar Field
• Nonperfect Carrollian Fluids Through Holography
• Shaving off soft hairs and the black hole image memory effect