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

TL;DR

This paper characterizes the spacetime flows that generate Hamiltonian dynamics in the space of initial data for asymptotically Kerr-de Sitter spacetimes and explores implications for black-hole thermodynamics.

Contribution

It identifies all flows leading to Hamiltonian dynamics in the space of initial data for asymptotically Kerr-de Sitter spacetimes and computes the associated Hamiltonians.

Findings

All spacetime flows with Hamiltonian dynamics in this setting are determined.

Explicit Hamiltonians for these flows are calculated.

Implications for black-hole thermodynamics are discussed.

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.