Related papers: Initial data and black holes for matter models
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…
Non-continuous "jumps" of Apparent Horizons occur generically in 3+1 (binary) black hole evolutions. The dynamical trapping horizon framework suggests a spacetime picture in which these "Apparent Horizon jumps" are understood as spatial…
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…
The purpose of the paper is to understand a mechanism of evolutionary formation of trapped surfaces when there is an electromagnetic field coupled to the background space-time. Based on the short pulse ansatz, on a given finite outgoing…
The subject of this work is the formation of black holes in pure general relativity, by the focusing of incoming gravitational waves. The theorems established in this monograph constitute the first foray into the long time dynamics of…
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…
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…
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 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 consider the spherically symmetric, asymptotically flat Einstein-Vlasov system. We find explicit conditions on the initial data, with ADM mass M, such that the resulting spacetime has the following properties: there is a family of…
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…
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…
Generalizing earlier results on the initial data and the final fate of dust collapse, we study here the relevance of the initial state of a spherically symmetric matter cloud towards determining its end state in the course of a continuing…
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.
In a recent important breakthrough D. Christodoulou has solved a long standing problem of General Relativity of evolutionary formation of trapped surfaces in the Einstein-vacuum space-times. He has identified an open set of regular initial…
We discuss the existence of asymptotically Euclidean initial data sets to the vacuum Einstein field equations which would give rise (modulo an existence result for the evolution equations near spatial infinity) to developments with a past…
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…
Building on the insight that primordial black holes can arise from the formation and subsequent gravitational collapse of bound states of stable supermassive elementary particles during the early radiation era, we offer a comprehensive…
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…
Primordial black holes, which could have been formed in the very early Universe due to the collapse of large curvature fluctuations, are nowadays one of the most attractive and fascinating research areas in cosmology for their possible…