On the uniqueness and global dynamics of AdS spacetimes

TL;DR

This paper proves that complete, non-singular asymptotically locally AdS spacetimes with stationary conformal infinity are globally stationary if they are asymptotically stationary in the past and future, establishing rigidity results.

Contribution

It demonstrates a uniqueness theorem for AdS spacetimes, showing global stationarity under specific asymptotic conditions, extending understanding of their global structure.

Findings

Any such spacetime is globally stationary if asymptotically stationary in past and future.

Provides rigidity results for exact AdS and related spacetimes.

Establishes conditions under which AdS spacetimes are uniquely determined by their asymptotic behavior.

Abstract

We study global aspects of complete, non-singular asymptotically locally AdS spacetimes solving the vacuum Einstein equations whose conformal infinity is an arbitrary globally stationary spacetime. It is proved that any such solution which is asymptotically stationary to the past and future is itself globally stationary. This gives certain rigidity or uniqueness results for exact AdS and related spacetimes.