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The positive energy theorem for weighted asymptotically anti-de Sitter spacetimes

Yaohua Wang, Xiao Zhang

Abstract

The positive energy theorem for weighted asymptotically flat spin manifolds was proved by Baldauf and Ozuch \cite{BO}, and for non-spin case by Chu and Zhu \cite{CZh}. In this paper, we generalize the positive energy theorem for 3-dimensional asymptotically anti-de Sitter initial data sets to weighted asymptotically anti-de Sitter initial data sets assuming that the weighted dominant energy condition holds.

The positive energy theorem for weighted asymptotically anti-de Sitter spacetimes

Abstract

The positive energy theorem for weighted asymptotically flat spin manifolds was proved by Baldauf and Ozuch \cite{BO}, and for non-spin case by Chu and Zhu \cite{CZh}. In this paper, we generalize the positive energy theorem for 3-dimensional asymptotically anti-de Sitter initial data sets to weighted asymptotically anti-de Sitter initial data sets assuming that the weighted dominant energy condition holds.
Paper Structure (5 sections, 9 theorems, 95 equations)

This paper contains 5 sections, 9 theorems, 95 equations.

Table of Contents

  1. Introduction
  2. Weighted total energy-momenta
  3. Energy-momentum endomorphism
  4. Weighted positive energy theorem
  5. Appendix: Killing vectors for the anti-de Sitter spacetime

Key Result

Proposition 2.1

where

Theorems & Definitions (13)

  • Definition 2.1
  • Definition 2.2
  • Proposition 2.1
  • Definition 3.1
  • Proposition 3.1
  • Lemma 4.1
  • Lemma 4.2
  • Lemma 4.3
  • Proposition 4.1
  • Proposition 4.2
  • ...and 3 more