Related papers: A simple construction of initial data for multiple…
Solving Einstein's constraint equations for the construction of black hole initial data requires handling the black hole singularity. Typically, this is done either with the excision method, in which the black hole interior is excised from…
The construction of initial-data sets representing binary black-hole configurations in quasi-circular orbits is studied in the context of the conformal-imaging formalism. An effective-potential approach for locating quasi-circular orbits is…
We present a novel model-independent generic mechanism for primordial black hole formation within the context of non-singular matter bouncing cosmology. In particular, considering a short duration transition from the matter contracting…
A general relativistic, stationary and axisymmetric black hole in a four-dimensional asymptotically-flat spacetime is fully determined by its mass, angular momentum and electric charge. The expectation that astrophysically relevant black…
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…
I describe the construction of initial data for the Einstein vacuum equations that can represent a collision of two black holes. I stress in the main physical ideas.
The parabolic-hyperbolic form of the constraints is integrated numerically. The applied numerical stencil is $4^{th}$ order accurate (in the spatial directions) while 'time'-integration is made by using the method of lines with a $4^{th}$…
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…
Non-static, spherically symmetric clusters of counter-rotating particles, of the type first introduced by Einstein, are analysed here. The initial data space can be parameterized in terms of three arbitrary functions, namely; initial…
Conformal mappings of surfaces of constant mean curvature onto compact bounded background spaces are constructed for Minkowski space-time and for Schwarzschild black hole spacetimes. In the black hole example, it is found that initial data…
Numerical relativity codes now being developed will evolve initial data representing colliding black holes at a relatively late stage in the collision. The choice of initial data used for code development has been made on the basis of…
We describe a procedure for constructing initial data for boosted black holes in the moving-punctures approach to numerical relativity that endows the initial time slice from the outset with trumpet geometry within the black hole interiors.…
We calculate puncture initial data corresponding to both single and binary black hole solutions of the constraint equations by means of a pseudo-spectral method applied in a single spatial domain. Introducing appropriate coordinates, these…
An attempt to construct the ``ground state'' vacuum initial data for the gravitational field surrounding two black holes is presented. The ground state is defined as the gravitational initial data minimizing the ADM mass within the class of…
We revisit the construction of puncture black hole initial data in the conformal thin-sandwich decomposition of Einstein's constraint equations. It has been shown previously that this approach cannot yield quasiequilibrium wormhole data,…
Spacetime is foliated by spatial hypersurfaces in the 3+1 split of General Relativity. The initial value problem then consists of specifying initial data for all relevant fields on one such a spatial hypersurface. These fields are the…
We consider the Einstein-Maxwell system as a Cauchy initial value problem taking the electric and magnetic fields as independent variables. Maxwell's equations in curved spacetimes are derived in detail using a 3+1 formalism and their…
Recently, a variational principle has been derived from Einstein-Hilbert and a matter Lagrangian for the spherically symmetric system of a dust shell and a black hole. The so-called physical region of the phase space, which contains all…
We investigate the spontaneous creation of primordial black holes in a lower-dimensional expanding early universe. We use the no-boundary proposal to construct instanton solutions for both the background and a black hole nucleated inside…
An open problem in general relativity has been to construct an asymptotically flat solution to a reasonable Einstein-matter system containing a black hole in the future and yet past-causally geodesically complete, in particular, containing…