MG12 - Talk detail
 

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Abstract

Post-Minkowskian Closed-Form Hamiltonian for Gravitating N-Body Systems

The Hamiltonian for a system of relativistic bodies interacting by their gravitational field is found in the post-Minkowskian approximation, including all terms linear in the gravitational constant. It is given in a surprisingly simple closed form as a function of canonical variables describing the bodies only. The field is eliminated by solving inhomogeneous wave equations, applying transverse-traceless projections, and using the Routh functional. By including all special relativistic effects our Hamiltonian extends the results described in classical textbooks of theoretical physics. As an application, the scattering of relativistic objects is considered.

Boundary conditions for BSSN system

In numerical relativity, hyperbolic systems of the second-order in space, first-order in time (SOIS-FOIT) partial differential equations (PDEs) are of great importance. Namely, impressive results were obtained by several groups using so-called BSSN system belonging to this category. While the analysis of the first order in space systems had provided a method of construction of boundary conditions compatible with PDEs, no such recipe is available for SOIS-FOIT systems unless it is symmetric hyperbolic. We show, that introducing potentials for evolution variables of linearized BSSN system, one can find an associated symmetric-hyperbolic systems of PDEs which provides boundary conditions for the original SOIS-FOIT BSSN system.

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