Related papers: Equilibrium initial data for moving puncture simul…
We analyze stationary slicings of the Schwarzschild spacetime defined by members of the Bona-Masso family of slicing conditions. Our main focus is on the influence of a non-vanishing offset to the extrinsic curvature, which forbids the…
We construct approximate analytical solutions to the constraint equations of general relativity for binary black holes of arbitrary mass ratio in quasicircular orbit. We adopt the puncture method to solve the constraint equations in the…
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…
Numerical relativity, applied to collisions of black holes, starts with initial data for black holes already in each other's strong field. The initial hypersurface data typically used for computation is based on mathematical simplifying…
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…
We construct a black hole initial data for the Einstein equations with prescribed scalar curvature, or more precisely a piece of initial data contained inside the black hole. The constraints translate into a parabolic equation, with radius…
Construction of binary black hole initial data is a prerequisite for numerical evolutions of binary black holes. This paper reports improvements to the binary black hole initial data solver in the Spectral Einstein Code, to allow robust…
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…
We develop a method to compute low-eccentricity initial data of black hole--neutron star binaries in the puncture framework extending previous work on other types of compact binaries. In addition to adjusting the orbital angular velocity of…
Binary black hole spacetimes with a helical Killing vector, which are discussed as an approximation for the early stage of a binary system, are studied in a projection formalism. In this setting the four dimensional Einstein equations are…
We construct a sequence of binary black hole puncture data derived under the assumptions (i) that the ADM mass of each puncture as measured in the asymptotically flat space at the puncture stays constant along the sequence, and (ii) that…
A numerical solution scheme for the Einstein field equations based on generalized harmonic coordinates is described, focusing on details not provided before in the literature and that are of particular relevance to the binary black hole…
We present numerical evolutions of three equal-mass black holes using the moving puncture approach. We calculate puncture initial data for three black holes solving the constraint equations by means of a high-order multigrid elliptic…
We consider the initial data problem for several black holes in vacuum with arbitrary momenta and spins on a three space with punctures. We compactify the internal asymptotically flat regions to obtain a computational domain without inner…
While the 1+log slicing condition has been extremely successful in numerous numerical relativity simulations, it is also known to develop "gauge-shocks" in some examples. Alternative "shock-avoiding" slicing conditions suggested by…
We present improvements to construction of binary black hole initial data used in SpEC (the Spectral Einstein Code). We introduce new boundary conditions for the extended conformal thin sandwich elliptic equations that enforce the excision…
The starting point of any general relativistic numerical simulation is a solution of the Hamiltonian and momentum constraints that (ideally) represents an astrophysically realistic scenario. We present a new method to produce initial data…
We construct initial data corresponding to a single perturbed Kerr black hole in vacuum. These data are defined on specific hyperboloidal ("ACMC-") slices on which the mean extrinsic curvature K asymptotically approaches a constant at…
We present a new initial data formulation to solve the full set of Einstein equations for spacetimes that contain a black hole under general conditions. The method can be used to construct complete initial data for spacetimes (the full…
Solving the 4-d Einstein equations as evolution in time requires solving equations of two types: the four elliptic initial data (constraint) equations, followed by the six second order evolution equations. Analytically the constraint…