Hyperbolic Hamiltonian equations for general relativity
Abstract
Description
The 3+1 Hamiltonian formulation in the gauge $D_tN=-K$ on the lapse function fixes the direction of time associated with the trace $K$ of the extrinsic curvature tensor. The Hamiltonian equations hereby become hyperbolic. We study this new system for black hole spacetimes that are asymptotically quiescent, which introduces analyticity properties that can be exploited for numerical calculations by compactification in spherical coordinates with complex radius following a Möbius transformation. Conformal flat initial data of two black holes are hereby invariant, and correspond to a turn point in a pendulum, up for a pair of separated black holes and down for a single black hole. Here, Newton's law appears in the relaxation of $l=2$ deformations of semi-infinite poloidal surface elements, defined by the moment of inertia of the binary.
Based on an invited talk at the Federation Denis Poisson (October 2008)
Based on an invited talk at the Federation Denis Poisson (October 2008)