Related papers: On the existence of initial data containing isolat…
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 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 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 show the existence of complete, asymptotically flat Cauchy initial data for the vacuum Einstein field equations, free of trapped surfaces, whose future development must admit a trapped surface. Moreover, the datum is exactly a constant…
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…
Isolated horizon conditions enforce the time invariance of both the intrinsic and the extrinsic geometry of a (quasilocal) black hole horizon. Nonexpanding horizons, only requiring the invariance of the intrinsic geometry, have been…
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…
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…
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…
The Einstein constraint equations describe the space of initial data for the evolution equations, dictating how space should curve within spacetime. Under certain assumptions, the constraints reduce to a scalar quasilinear parabolic…
We present a new scheme for constructing initial data for the Einstein field equations using the conformal thin-sandwich formulation that does not assume conformal flatness or approximate Killing vectors. This includes a method for…
Initial data for the spherically symmetric Einstein-Vlasov system is constructed whose past evolution is regular and whose future evolution contains a black hole. This is the first example of initial data with these properties for the…
Initial data are the starting point for any numerical simulation. In the case of numerical relativity, Einstein's equations constrain our choices of these initial data. We will examine several of the formalisms used for specifying Cauchy…
A complete formalism for constructing initial data representing black-hole binaries in quasi-equilibrium is developed. Radiation reaction prohibits, in general, true equilibrium binary configurations. However, when the timescale for orbital…
This paper treats boundary conditions on black hole horizons for the full 3+1D Einstein equations. Following a number of authors, the apparent horizon is employed as the inner boundary on a space slice. It is emphasized that a further…
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,…
Initial data corresponding to spacetimes containing black holes are considered in the time symmetric case. The solutions are obtained by matching across the apparent horizon different, conformally flat, spatial metrics. The exterior metric…
The Cauchy problem of the vacuum Einstein's equations aims to find a semi-metric $g_{\alpha\beta}$ of a spacetime with vanishing Ricci curvature $R_{\alpha,\beta}$ and prescribed initial data. Under the harmonic gauge condition, the…
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…
Einstein's equations are known to lead to the formation of black holes and spacetime singularities. This appears to be a manifestation of the mathematical phenomenon of finite-time blowup: a formation of singularities from regular initial…