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