Energy in higher-dimensional Spacetimes

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Written by Hamed Barzegar

Based on the geometric Hamiltonian formalism we derive new expressions for the total Hamiltonian energy of gravitating systems in higher dimensions in terms of the Riemann tensor, allowing a cosmological constant. In this way, we also obtain the ADM and the Komar expressions of the corresponding spacetimes. We then apply this analysis to a large class of higher dimensional spacetimes with various asymptotics known to us, which satisfy certain conditions. In particular, our analysis covers asymptotically flat spacetimes, Kaluza-Klein asymptotically flat spacetimes, as well as asymptotically (anti-)de Sitter spacetimes. As it turns out, the Komar mass equals the ADM mass in stationary asymptotically flat spacetimes in all dimensions, generalizing the four-dimensional result of Beig. We show that in general, the Hamiltonian mass, the ADM mass and the Komar mass do not coincide with each other in the non-asymptotically flat setting.
 
This talk is based on my master's thesis under supervision of Prof. P. T. Chrusciel.