Hamiltonian dynamics in the space of asymptotically Kerr–de Sitter spacetimes

Abstract

We determine all spacetime flows which lead to a Hamiltonian dynamics in the space of general relativistic initial data sets with asymptotically Kerr-de Sitter ends. The corresponding Hamiltonians are calculated. Some implications for black-hole thermodynamics are pointed out.

A review of total energy–momenta in GR with a positive cosmological constant

“…In this subsection we review their work on asymptotically-Schwarzschild-de Sitter data and asymptotically-Kerr-de Sitter data. These are discussed in [60] and [61] respectively and these in turn rely on families of initial data for the Einstein equations shown to exist in [62] and [63] respectively. The Schwarzschild-de Sitter metric, sometimes called the Kottler solution, can be defined in space-time dimension n + 1 as…”

“…Again one has an infinite periodic metric but now with a particular nonzero periodic second fundamental form as well. Then in [61], the authors use the Hamiltonian method to assign both mass and angular momentum to these data.…”

The Euclidean quantisation of Kerr-Newman-de Sitter black holes

“…While we suspect that these are all possibilities, we have not made in-depth attempts to analyse whether or not the list below is exhaustive. 3 Note that oriented manifolds are obtained if and only if ω 2 = α 1 α 2 ω.…”

“…In a Hamiltonian approach this ambiguity is related to the choice of the Killing vector field for which we calculate the Hamiltonian [3]. In any case, the physical mass M phys and the angular momentum J phys are usually calculated using the formulae Figure 7.…”

“…Here M phys = M/(1 + λa 2 ) 2 is the physical mass of the Lorentzian partner solution (compare [3,9]), |J phys | = aM/(1 + λa 2 ) is the Komar angular momentum of the Lorentzian partner solution, and |q phys | := p 2 eff /(1 + λa 2 ) is the total magnetic Maxwell charge of the Lorentzian solution with e = 0 (compare [19]). …”