Related papers: A simple construction of initial data for multiple…
We construct initial data for several black holes with arbitrary momenta and spins by a new method that is based on a compactification of Brill-Lindquist wormholes. When treated numerically, the method leads to a significant simplification…
We present approximate analytical solutions to the Hamiltonian and momentum constraint equations, corresponding to systems composed of two black holes with arbitrary linear and angular momentum. The analytical nature of these initial data…
We explore whether a new method to solve the constraints of Einstein's equations, which does not involve elliptic equations, can be applied to provide initial data for black holes. We show that this method can be successfully applied to a…
We solve for single distorted black hole initial data using the puncture method, where the Hamiltonian constraint is written as an elliptic equation in R^3 for the nonsingular part of the metric conformal factor. With this approach we can…
We discuss the initial value problem of general relativity in its recently unified Lagrangian and Hamiltonian pictures and present a multi-domain pseudo-spectral collocation method to solve the resulting coupled nonlinear partial…
To observe the dynamic formation of black holes in general relativity, one essentially needs to prove that closed trapped surfaces form during evolution from initial data that do not already contain trapped surfaces. We discuss the recent…
We generalize Bowen-York black hole initial data to hyperboloidal constant mean curvature slices which extend to future null infinity. We solve this initial value problem numerically for several cases, including unequal mass binary black…
We present a general construction of initial data for Einstein's equations containing an arbitrary number of black holes, each of which is instantaneously in equilibrium. Each black hole is taken to be a marginally trapped surface and plays…
We construct a family of asymptotically flat Cauchy initial data for the Einstein vacuum equations that contain no trapped surfaces, yet whose future development admits multiple causally independent trapped surfaces. Assuming the weak…
We present approximate analytical solutions to the Hamiltonian and momentum constraint equations, corresponding to systems composed of two black holes with arbitrary linear and angular momentum. The analytical nature of these initial data…
We propose a new approach, based on the puncture method, to construct black hole initial data in the so-called trumpet geometry, i.e. on slices that asymptote to a limiting surface of non-zero areal radius. Our approach is easy to implement…
The standard approach to initial data for both analytic and numerical computations of black hole collisions has been to use conformally-flat initial geometry. Among other advantages, this choice allows the simple superposition of holes with…
In this paper we investigate the parabolic-hyperbolic formulation of the vacuum constraint equations introduced by R{\'a}cz with a view to constructing multiple black hole initial data sets without spin. In order to respect the natural…
We review in a pedagogical fashion the 3+1-split which serves to put Einstein's equations into the form of a dynamical system with constraints. We then discuss the constraint equations under the simplifying assumption of time-symmetry.…
In backgrounds with compact dimensions there may exist several phases of black objects including the black-hole and the black-string. The phase transition between them raises puzzles and touches fundamental issues such as topology change,…
We give a simple construction of smooth, asymptotically flat vacuum initial data modeling a relativistic collapsing $N$--body system, with independently prescribed ADM energy, linear momentum, and angular momentum for each component,…
We present a set of boundary conditions for solving the elliptic equations in the Initial Data Problem for space-times containing a black hole, together with a number of constraints to be satisfied by the otherwise freely specifiable…
We obtain an explicit solution of the momentum constraint for conformally flat, maximal slicing, initial data which gives an alternative to the purely longitudinal extrinsic curvature of Bowen and York. The new solution is related, in a…
We present a new approach for setting initial Cauchy data for multiple black hole spacetimes. The method is based upon adopting an initially Kerr-Schild form of the metric. In the case of non-spinning holes, the constraint equations take a…
We construct initial data suitable for the Kerr stability conjecture, that is, solutions to the constraint equations on a spacelike hypersurface with boundary entering the black hole horizon that are arbitrarily decaying perturbations of a…