Linearized perturbations of the Kerr spacetime and outer boundary conditions in numerical relativity

E Deadman (1) , J M Stewart (1)

1 Department of Applied Mathematics & Theoretical Physics Centre for Mathematical Sciences

This paper discusses linearised vacuum gravitational perturbations of the Kerr spacetime in a neighbourhood of future null infinity I +. Unlike earlier discussion of perturbations of the Kerr space-time we avoid the use of spheroidal harmonics and harmonic time dependence. Instead we develop the theory in terms of Hertz potentials and spherical harmonics with coupling between modes. The " master equation " is a single complex scalar wave equation which, in the Minkowski limit, reduces to the Euler-Poisson-Darboux equation. We solve this by Picard iteration making extensive use of the flat space-time Riemann-Green function. As an application we consider the problem of outer boundary conditions for numerical relativity and generalise earlier results of Buchman & Sarbach (2006), (2007) for the Schwarzschild case.

Mots clés: Physical Sciences

E Deadman, J M Stewart. Linearized perturbations of the Kerr spacetime and outer boundary conditions in numerical relativity. Classical and Quantum Gravity, 2011, 28 (1), pp.15003. ⟨10.1088/0264-9381/28/1/015003⟩. ⟨hal-00657596⟩