2017/08/31 by Hamed Barzegar, Piotr T. Chruściel, Michael Hörzinger · 10 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Cosmological constant #Cosmology and Gravitation Theories #Hamiltonian (control theory) #Kaluza–Klein theory #Mathematical analysis #Mathematical physics #Mathematics #Negative mass #Noncommutative and Quantum Gravity Theories #Physics #Quantum mechanics #Riemann hypothesis #Spacetime #gr-qc
paper · pdf · doi:10.1103/physrevd.96.124002
published in Physical review. D/Physical review. D. 96(12) (American Physical Society)
openalex publication_date 2017/12/01 · arxiv created 2017/12/20 · arxiv updated 2017/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
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 \mathrm\ensuremathΛ\ensuremath∈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.