Related papers: Cauchy problem as a two-surface based `geometrodyn…
It is shown that a spacetime with collisionless matter evolving from data on a compact Cauchy surface with hyperbolic symmetry can be globally covered by compact hypersurfaces on which the mean curvature is constant and by compact…
We consider a system representing self-gravitating balls of dust in an expanding Universe. It is demonstrated that one can prescribe data for such a system at infinity and evolve it backward in time without the development of shocks or…
We investigate the two-dimensional behavior of gravity coupled to a dynamical unit timelike vector field, i.e. "Einstein-aether theory". The classical solutions of this theory in two dimensions depend on one coupling constant. When this…
An algebraic-hyperbolic method for solving the Hamiltonian and momentum constraints has recently been shown to be well posed for general nonlinear perturbations of the initial data for a Schwarzschild black hole. This is a new approach to…
We establish a variant, which has the advantage of introducing only physical characteristics, of the symmetric quasi linear first order system given by H.\ Friedrich for the evolution equations of gravitating fluid bodies in General…
In this article the unique solution of the Cauchy problem is founded by the Riemann method. Some relations for given here confluent hypergeometric functions of two and three variables are used.
This is the author Master's Thesis and its main purpose is to demonstrate that it is possible to formulate Einstein's field equations as an initial value problem. The first chapter concerns the hyperbolic equations theory. The definition of…
We have recently proposed in \cite{Park:2014tia} the quantization of pure 4D Einstein gravity through hypersurface foliation, and observed that the 4D Einstein gravity becomes renormalizable once all (or most) of the unphysical degrees of…
Numerical solutions of Einstein's and scalar-field equations are found for a global defect in a higher-dimensional spacetime. The defect has a $(3+1)$-dimensional core and a ``hedgehog'' scalar-field configuration in $n=3$ extra dimensions.…
Various aspects of the Cauchy problem for the Einstein equations are surveyed, with the emphasis on local solutions of the evolution equations. Particular attention is payed to giving a clear explanation of conceptual issues which arise in…
In a former paper we proposed a model for the quantization of gravity by working in a bundle $E$ where we realized the Hamilton constraint as the Wheeler-DeWitt equation. However, the corresponding operator only acts in the fibers and not…
In this paper, we consider the initial value problem for the Einstein-Vlasov-Scalar field equations in temporal gauge, where the initial data are prescribed on two characteristic smooth intersecting hypersurfaces. From a suitable choice of…
We study Cosmological Einsteinian Cubic Gravity (CECG) arXiv:1810.08166v3 in the context of minisuperspace quantum cosmology. CECG is a modification of Einstein's gravity by cubic curvature terms that yield a nontrivial contribution to the…
The 3+1 (canonical) decomposition of all geometries admitting two-dimensional space-like surfaces is exhibited. A proposal consisting of a specific re-normalization {\bf Assumption} and an accompanying {\bf Requirement} is put forward,…
A Cauchy-characteristic initial value problem for the Einstein-Klein-Gordon system with spherical symmetry is presented. Initial data are specified on the union of a space-like and null hypersurface. The development of the data is obtained…
Self-accelerating backgrounds in massive gravity provide an arena to explore the Cauchy problem for derivatively coupled fields that obey complex constraints which reduce the phase space degrees of freedom. We present here an algorithm…
Strongly coupled gravitational systems describe Einstein gravity and matter in the limit that Newton's constant G is assumed to be very large. The nonlinear evolution of these systems may be solved analytically in the classical and…
We construct explicitly a (12g-12)-dimensional space P of unconstrained and independent initial data for 't Hooft's polygon model of (2+1) gravity for vacuum spacetimes with compact genus-g spacelike slices, for any g >= 2. Our method…
The purpose of this paper is to demonstrate a new method of generating exact solutions to the Einstein's equations obtained by the Hamiltonian reduction. The key element to the successful Hamiltonian reduction is finding the privileged…
The curvature-squared model of gravity, in the affine form proposed by Weyl and Yang, is deduced from a topological action in 4D. More specifically, we start from the Pontrjagin (or Euler) invariant. Using the BRST antifield formalism with…