35 research outputs found
A Hamiltonian Approach to the Mass of Isolated Black Holes
Boundary conditions defining a non-rotating isolated horizon are given in
Einstein-Maxwell theory. A spacetime representing a black hole which itself is
in equilibrium but whose exterior contains radiation admits such a horizon.
Inspired by Hamiltonian mechanics, a (quasi-)local definition of isolated
horizon mass is formulated. Although its definition does not refer to infinity,
this mass takes the standard value in a Reissner-Nordstrom solution.
Furthermore, under certain technical assumptions, the mass of an isolated
horizon is shown to equal the future limit of the Bondi energy.Comment: 5 pages, LaTeX 2.09, 1 eps figure. To appear in the proceedings of
the Eighth Canadian Conference on General Relativity and Relativistic
Astrophysic
Isolated Horizons: A Generalization of Black Hole Mechanics
A set of boundary conditions defining a non-rotating isolated horizon are
given in Einstein-Maxwell theory. A space-time representing a black hole which
itself is in equilibrium but whose exterior contains radiation admits such a
horizon . Physically motivated, (quasi-)local definitions of the mass and
surface gravity of an isolated horizon are introduced. Although these
definitions do not refer to infinity, the quantities assume their standard
values in Reissner-Nordstrom solutions. Finally, using these definitions, the
zeroth and first laws of black hole mechanics are established for isolated
horizons.Comment: 9 pages, LaTeX2e, 3 eps figure
Towards a novel wave-extraction method for numerical relativity. I. Foundations and initial-value formulation
The Teukolsky formalism of black hole perturbation theory describes weak
gravitational radiation generated by a mildly dynamical hole near equilibrium.
A particular null tetrad of the background Kerr geometry, due to Kinnersley,
plays a singularly important role within this formalism. In order to apply the
rich physical intuition of Teukolsky's approach to the results of fully
non-linear numerical simulations, one must approximate this Kinnersley tetrad
using raw numerical data, with no a priori knowledge of a background. This
paper addresses this issue by identifying the directions of the tetrad fields
in a quasi-Kinnersley frame. This frame provides a unique, analytic extension
of Kinnersley's definition for the Kerr geometry to a much broader class of
space-times including not only arbitrary perturbations, but also many examples
which differ non-perturbatively from Kerr. This paper establishes concrete
limits delineating this class and outlines a scheme to calculate the
quasi-Kinnersley frame in numerical codes based on the initial-value
formulation of geometrodynamics.Comment: 11 pages, 1 figur
Eigenspectral computtations for linear gravity and nonlinear toy models
Journal ArticleThe periodic standing-wave approach to binary inspiral assumes rigid rotation of gravitational fields and hence helically symmetric solutions. To exploit the symmetry, numerical computations must solve for "helical scalars," fields that are functions only of corotating coordinates, the labels on the helical Killing trajectories. Here we present the formalism for describing linearized general relativity in terms of helical scalars and we present solutions to the mixed partial differential equations of the linearized gravity problem (and to a toy nonlinear problem) using the adapted coordinates and numerical techniques previously developed for scalar periodic standing-wave computations. We argue that the formalism developed may suffice for periodic standing-wave computations for post-Minkowskian computations and for full general relativity
Periodic standing-wave approzimation: post-Minkowski computations
Journal ArticleThe periodic standing-wave method studies circular orbits of compact objects coupled to helically symmetric standing-wave gravitational fields. From this solution an approximation is extracted for the strong field, slowly inspiralling motion of black holes and binary stars. Previous work on this model has dealt with nonlinear scalar models, and with linearized general relativity. Here we present the results of the method for the post-Minkowski (PM) approximation to general relativity, the first step beyond linearized gravity. We compute the PM approximation in two ways: first, via the standard approach of computing linearized gravitational fields and constructing from them quadratic driving sources for second-order fields, and second, by solving the second-order equations as an "exact" nonlinear system. The results of these computations have two distinct applications: (i) The computational infrastructure for the exact PM solution will be directly applicable to full general relativity. (ii) The results will allow us to begin supplying initial data to collaborators running general relativistic evolution codes
The periodic standing-wave approximation: eigenspectral computations for linear gravity and nonlinear toy models
The periodic standing wave approach to binary inspiral assumes rigid rotation
of gravitational fields and hence helically symmetric solutions. To exploit the
symmetry, numerical computations must solve for ``helical scalars,'' fields
that are functions only of corotating coordinates, the labels on the helical
Killing trajectories. Here we present the formalism for describing linearized
general relativity in terms of helical scalars and we present solutions to the
mixed partial differential equations of the linearized gravity problem (and to
a toy nonlinear problem) using the adapted coordinates and numerical techniques
previously developed for scalar periodic standing wave computations. We argue
that the formalism developed may suffice for periodic standing wave
computations for post-Minkowskian computations and for full general relativity.Comment: 21 pages, 10 figures, RevTe
Towards wave extraction in numerical relativity: the quasi-Kinnersley frame
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 non-perturbatively 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.Comment: 13 pages, 3 figure