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The conformal formulation of the Einstein constraint equations is first reviewed, and we then consider the design, analysis, and implementation of adaptive multilevel finite element-type numerical methods for the resulting coupled nonlinear…
We study stress tensor correlation functions in four-dimensional conformal field theories with large $N$ and a sparse spectrum. Theories in this class are expected to have local holographic duals, so effective field theory in anti-de Sitter…
The issue of the physical equivalence between the different coordinate system in Einstein theory is revised. Gauge fixing influences results of measurements and physics are different in two different coordinate system. Spacetime metric…
The leading $(\alpha')^3$-correction to the gravitational low-energy effective action of closed (type II) superstring theory in four-spacetime dimensions defines the Einstein-Grisaru-Zanon gravity action that is applied for a calculation of…
A Green's function method is developed for solving strongly-coupled gravity and matter in the semiclassical limit. In the strong-coupling limit, one assumes that Newton's constant approaches infinity. As a result, one may neglect second…
We develop here a new procedure within Einstein's theory of gravity to generate equilibrium configurations that result as the final state of gravitational collapse from regular initial conditions. As a simplification, we assume that the…
In this paper we provide a method capable of producing an infinite number of solutions for Einstein's equation on static spacetimes with perfect fluid as a matter field. All spacetimes of this type which are symmetric with respect to a…
We develop a gluing construction which adds scaled and truncated asymptotically Euclidean solutions of the Einstein constraint equations to compact solutions with potentially non-trivial cosmological constants. The result is a one-parameter…
We describe a post-Minkowskii approximation of general relativity as a power series expansion in G, Newton's gravitational constant. Material sources are hidden behind boundaries, and only the vacuum Einstein equations are considered. An…
We derive noncommutative Einstein equations for abelian twists and their solutions in consistently symmetry reduced sectors, corresponding to twisted FRW cosmology and Schwarzschild black holes. While some of these solutions must be…
We study soft limits of correlation functions for the density and velocity fields in the theory of structure formation. First, we re-derive the (resummed) consistency conditions at unequal times using the eikonal approximation. These are…
In general relativity, traversable wormholes are possible provided they do not represent shortcuts in the spacetime. Einstein equations, together with the achronal averaged null energy condition, demand to take longer for an observer to go…
A rotating metric solution in Einstein-Gauss-Bonnet gravity with a negative cosmological constant was recently found in the Chern-Simons point. We construct a rotating thin shell gluing two spacetimes in Einstein-Gauss-Bonnet gravity, using…
Recent work has studied the thermodynamics of gravity subjected to conformal boundary conditions, where the trace of the extrinsic curvature $K$ and the conformal class of metrics are kept fixed. The case $K < 0$ seems tied to solutions…
Problems of particle dynamics involving unsteady Stokes flows in confined geometries are typically harder to solve than their steady counterparts. Approximation techniques are often the only resort. Felderhof (see e.g. 2005, 2009b) has…
This paper explores ``black hole'' solutions of various Einstein-wave matter systems admitting an isometry of their domain of outer communications taking every point to its future. In the first two parts, it is shown that such solutions,…
We prove that the Einstein equations can be solved in a very general form for arbitrary spacetime dimensions and various types of vacuum and non-vacuum cases following a geometric method of anholonomic frame deformations for constructing…
We investigate the solutions of Einstein equations such that a hedgehog solution is matched to different exterior or interior solutions via a spherical shell. In the case where both the exterior and the interior regions are hedgehog…
We consider Einstein Gravity coupled to dynamical matter consisting of a gauge field with any compact gauge group and minimally coupled scalar fields. We investigate the conditions under which a free specification of a spatial field…
We investigate the necessary conditions for the two spacetimes, which are solutions to the Einstein field equations with an anisotropic matter source, to be related to each other by means of a conformal transformation. As a result, we…