Related papers: Affine-null metric formulation of General Relativi…
The characteristic initial (boundary) value problem has numerous applications in general relativity (GR) involving numerical studies, and is often formulated using Bondi-like coordinates. Recently it was shown that several prototype…
In regards to the initial-boundary value problem of the Einstein equations, we argue that the projection of the Einstein equations along the normal to the boundary yields necessary and appropriate boundary conditions for a wide class of…
The hyperboloidal initial value problem is addressed in the context of Numerical Relativity, motivated by its use of hyperboloidal slices - smooth spacelike slices that reach future null infinity, the "place" in spacetime where radiation is…
A strongly well-posed initial boundary value problem based upon constraint-preserving boundary conditions of the Sommerfeld type has been established for the harmonic formulation of the vacuum Einstein's equations. These Sommerfeld…
By employing the Bianchi identities for the Riemann tensor in conjunction with the Einstein equations, we construct a first order symmetric hyperbolic system for the evolution part of the Cauchy problem of general relativity. In this…
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…
Given any two Einstein (pseudo-)metrics, with scalar curvatures suitably related, we give an explicit construction of a Poincar\'e-Einstein (pseudo-)metric with conformal infinity the conformal class of the product of the initial metrics.…
We look for physically realistic initial data in numerical relativity which are in agreement with post-Newtonian approximations. We propose a particular solution of the time-symmetric constraint equation, appropriate to two momentarily…
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…
The formalism of hypersurface data is a framework to study hypersurfaces of any causal character abstractly (i.e. without the need of viewing them as embedded in an ambient space). In this paper we exploit this formalism to study the…
This review examines the role of differential forms, Pfaffian systems, and hypersurfaces in general relativity. These mathematical constructions provide the essential tools for general relativity, in which the curvature of…
We address the problem of consistent Campiglia-Laddha superrotations in $d>4$ by solving Bondi-Sachs gauge vacuum Einstein equations at the non-linear level with the most general boundary conditions preserving the null nature of infinity.…
General hypersurfaces of any causal character can be studied abstractly using the hypersurface data formalism. In the null case, we write down all tangential components of the ambient Ricci tensor in terms of the abstract data. Using this…
We reformulate the Einstein equations as equations for families of surfaces on a four-manifold. These surfaces eventually become characteristic surfaces for an Einstein metric (with or without sources). In particular they are formulated in…
A generalized symmetry of a system of differential equations is an infinitesimal transformation depending locally upon the fields and their derivatives which carries solutions to solutions. We classify all generalized symmetries of the…
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…
In the search for exact solutions to Einstein's field equations the main simplification tool is the introduction of spacetime symmetries. Motivated by this fact we develop a method to write the field equations for general matter in a form…
Here we have developed the general parametrization for spherically symmetric and asymptotically flat black-hole spacetimes in an arbitrary metric theory of gravity. The parametrization is similar in spirit to the parametrized post-Newtonian…
A generalized definition of a frame of reference in spaces with affine connections and metrics is proposed based on the set of the following differential-geometric objects: (a) a non-null (non-isotropic) vector field, (b) the orthogonal to…
A new class of time-symmetric solutions to the initial value constraints of vacuum General Relativity is introduced. These data are globally regular, asymptotically flat (with possibly several asymptotic ends) and in general have no…