TY - JOUR

T1 - Towards a wave-extraction method for numerical relativity. II. The quasi-Kinnersley frame

AU - Nerozzi, A.

AU - Beetle, C.

AU - Bruni, Marco

AU - Burko, L.

AU - Pollney, D.

PY - 2005/7/15

Y1 - 2005/7/15

N2 - The Newman-Penrose formalism may be used in numerical relativity to extract coordinate-invariant information about gravitational radiation emitted in strong-field dynamical scenarios. The main challenge in doing so is to identify a null tetrad appropriately adapted to the simulated geometry such that Newman-Penrose quantities computed relative to it have an invariant physical meaning. In black hole perturbation theory, the Teukolsky formalism uses such adapted tetrads, those which differ only perturbatively from the background Kinnersley tetrad. At late times, numerical simulations of astrophysical processes producing isolated black holes ought to admit descriptions in the Teukolsky formalism. However, adapted tetrads in this context must be identified using only the numerically computed metric, since no background Kerr geometry is known a priori. To do this, this paper introduces the notion of a quasi-Kinnersley frame. This frame, when space-time is perturbatively close to Kerr, approximates the background Kinnersley frame. However, it remains calculable much more generally, in space-times nonperturbatively different from Kerr. We give an explicit solution for the tetrad transformation which is required in order to find this frame in a general space-time

AB - The Newman-Penrose formalism may be used in numerical relativity to extract coordinate-invariant information about gravitational radiation emitted in strong-field dynamical scenarios. The main challenge in doing so is to identify a null tetrad appropriately adapted to the simulated geometry such that Newman-Penrose quantities computed relative to it have an invariant physical meaning. In black hole perturbation theory, the Teukolsky formalism uses such adapted tetrads, those which differ only perturbatively from the background Kinnersley tetrad. At late times, numerical simulations of astrophysical processes producing isolated black holes ought to admit descriptions in the Teukolsky formalism. However, adapted tetrads in this context must be identified using only the numerically computed metric, since no background Kerr geometry is known a priori. To do this, this paper introduces the notion of a quasi-Kinnersley frame. This frame, when space-time is perturbatively close to Kerr, approximates the background Kinnersley frame. However, it remains calculable much more generally, in space-times nonperturbatively different from Kerr. We give an explicit solution for the tetrad transformation which is required in order to find this frame in a general space-time

U2 - 10.1103/PhysRevD.72.024014

DO - 10.1103/PhysRevD.72.024014

M3 - Article

VL - 72

SP - 024014

JO - Physical Review D

JF - Physical Review D

SN - 1550-7998

IS - 2

ER -