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ON THE STRUCTURE OF ASYMPTOTICALLY DE SITTER AND ANTI-DE SITTER SPACES
 

Summary: ON THE STRUCTURE OF ASYMPTOTICALLY DE SITTER AND ANTI-DE
SITTER SPACES
MICHAEL T. ANDERSON
Abstract. We discuss several aspects of the relation between asymptotically AdS and asymptotically
dS spacetimes including: the continuation between these types of spaces, the global stability of asymp-
totically dS spaces and the structure of limits within this class, holographic renormalization, and the
maximal mass conjecture of Balasubramanian-deBoer-Minic.
1. Introduction.
This paper deals with several distinct issues on local and global aspects of asymptotically de Sitter
spaces and their anti-de Sitter or hyperbolic counterparts. Besides their intrinsic interest in classical
general relativity, asymptotically de Sitter spaces arise frequently in the context of in ationary models
and issues related to the cosmic no-hair conjecture [1], [2]. Moreover, they are of current interest
in attempts to understand a possible dS/CFT correspondence [3], [4] analogous to the much more
rigorously established AdS/CFT correspondence [5]-[7].
Asymptotically de Sitter (dS) spaces are understood here to be vacuum solutions to the Einstein
equations with  > 0 which to the future (or past), have geometry asymptotically approaching that of
pure de Sitter space locally. Globally, these spaces may be quite di erent than de Sitter; in particular
future space-like in nity I + may have arbitary topology and induced metric. Asymptotically anti-
de Sitter (AdS) or hyperbolic (AH) spaces are understood in the same sense; see x2 for the precise
de nitions.

  

Source: Anderson, Michael - Department of Mathematics, SUNY at Stony Brook

 

Collections: Mathematics