Abstract
We study the geometry of a general class of vacuum asymptotically anti-de Sitter spacetimes near the conformal boundary. In particular, the spacetime is only assumed to have finite regularity, and it is allowed to have arbitrary boundary topology and geometry. For the main results, we derive limits at the conformal boundary of various geometric quantities, and we use these limits to construct partial Fefferman–Graham expansions from the boundary. The results of this article will be applied, in upcoming papers, toward proving symmetry extension and gravity–boundary correspondence theorems for vacuum asymptotically anti-de Sitter spacetimes.
Highlights
Introduction pte dMThe main objective of this article is to study the geometry, near the timelike conformal boundary, of a wide class of asymptotically Anti-de Sitter spacetimes that satisfy the Einstein-vacuum equations
We study the geometry of a general class of vacuum asymptotically Anti-de Sitter spacetimes near the conformal boundary
(2) We apply these limits in order to construct partial Fefferman–Graham expansions from the conformal boundary for these same geometric quantities
Summary
The main objective of this article is to study the geometry, near the timelike conformal boundary, of a wide class of asymptotically Anti-de Sitter spacetimes that satisfy the Einstein-vacuum equations. The aAdS spacetimes obtained by solving the initial-boundary value problem for the Einstein-vacuum equations (for instance, in [10, 13]) satisfy these regularity criteria Given these very weak assumptions, the main results of this paper achieve the following:. Since the Einstein-vacuum equations and its ρ-derivatives, formulated in terms of vertical tensor fields, have the basic form (1.8), we can use the above observation in order to derive boundary limits for g and its derivatives. In these equations (see (2.31)), the corresponding constant c remains positive until one reaches the equation for ∂ρn g, for which c = 0. The work in this paper is supported by EPSRC grant EP/R011982/1
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
