Energy in higher-dimensional spacetimes

Author(s)
Hamed Barzegar, Piotr T. Chrusciel, Michael Hoerzinger
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.

Organisation(s)
Gravitational Physics, Research Platform Erwin Schrödinger International Institute for Mathematics and Physics
Journal
Physical Review D
Volume
96
No. of pages
25
ISSN
2470-0010
DOI
https://doi.org/10.1103/PhysRevD.96.124002
Publication date
12-2017
Peer reviewed
Yes
Austrian Fields of Science 2012
103028 Theory of relativity
Keywords
ASJC Scopus subject areas
Physics and Astronomy (miscellaneous)
Portal url
https://ucrisportal.univie.ac.at/en/publications/876161bf-8b16-4884-b0b4-a087ab4e6d82