Energy in higher-dimensional spacetimes

Hamed Barzegar, Piotr T. Chrusciel, Michael Hoerzinger

Publications: Contribution to journalArticlePeer Reviewed

Abstract

We derive expressions for the total Hamiltonian energy of gravitating systems in higher-dimensional theories in terms of the Riemann tensor, allowing a cosmological constant Λ R. Our analysis covers asymptotically anti-de Sitter spacetimes, asymptotically flat spacetimes, as well as Kaluza-Klein asymptotically flat spacetimes. We show that the Komar mass equals the Arnowitt-Deser-Misner (ADM) mass in stationary asymptotically flat spacetimes in all dimensions, generalizing the four-dimensional result of Beig, and that this is no longer true with Kaluza-Klein asymptotics. We show that the Hamiltonian mass does not necessarily coincide with the ADM mass in Kaluza-Klein asymptotically flat spacetimes, and that the Witten positivity argument provides a lower bound for the Hamiltonian mass - and not for the ADM mass - in terms of the electric charge. We illustrate our results on the five-dimensional Rasheed metrics, which we study in some detail, pointing out restrictions that arise from the requirement of regularity, which have gone seemingly unnoticed so far in the literature.

Original languageEnglish
Article number124002
Number of pages25
JournalPhysical Review D
Volume96
Issue number12
DOIs
Publication statusPublished - 1 Dec 2017

Austrian Fields of Science 2012

  • 103028 Theory of relativity

Keywords

  • ASYMPTOTICALLY HYPERBOLIC MANIFOLDS
  • DE-SITTER SPACETIMES
  • KALUZA-KLEIN THEORY
  • GENERAL-RELATIVITY
  • CONSERVED QUANTITIES
  • POSITIVE-ENERGY
  • BLACK-HOLES
  • COSMOLOGICAL CONSTANT
  • SPATIAL INFINITY
  • THEOREM

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