Asymptotic symmetries of projectively compact order one Einstein manifolds

Abstract

We show that the boundary of a projectively compact Einstein manifold of dimension $n$ can be extended by a line bundle naturally constructed from the projective compactification. This extended boundary is such that its automorphisms can be identified with asymptotic symmetries of the compactification. The construction is motivated by the investigation of a new curved orbit decomposition for a $n+1$ dimensional manifold which we prove results in a line bundle over a projectively compact order one Einstein manifolds.

arXiv commentThis is the version accepted for publication in Philosophical Transactions of the Royal Society A. It is part of a discussion meeting issue "At the interface of asymptotics, conformal methods and analysis in general relativity"

References in corpus (18)

• Conformal Carroll groups and BMS symmetry
• Carroll versus Newton and Galilei: two dual non-Einsteinian concepts of time
• Gauging the Carroll Algebra and Ultra-Relativistic Gravity
• Carroll versus Galilei Gravity
• Connections and dynamical trajectories in generalised Newton-Cartan gravity II. An ambient perspective
• Carrollian and celestial spaces at infinity
• Relaxing the Parity Conditions of Asymptotically Flat Gravity
• Embedding Galilean and Carrollian geometries I. Gravitational waves
• Carrollian manifolds and null infinity: A view from Cartan geometry
• Einstein metrics in projective geometry
• Asymptotic Shear and the Intrinsic Conformal Geometry of Null-Infinity
• Holonomy reductions of Cartan geometries and curved orbit decompositions
• Projective Compactifications and Einstein metrics
• Tractor geometry of asymptotically flat spacetimes
• Projective BGG equations, algebraic sets, and compactifications of Einstein geometries
• A comparison of Ashtekar's and Friedrich's formalisms of spatial infinity
• Projective Compactness and Conformal Boundaries
• Projective differential geometry and asymptotic analysis in General Relativity

Cited by in corpus (2)

• Projective and Carrollian geometry at time/space-like infinity on projectively compact Ricci flat Einstein manifolds
• Ti and Spi, Carrollian extended boundaries at timelike and spatial infinity