Related papers: Einstein's equation and geometric asymptotics
A classical model for the extension of singular spacetime geometries across their singularities is presented. The regularization introduced by this model is based on the following observation. Among the geometries that satisfy Einstein's…
Mathematical modeling of gravitating configurations of physical fields is one of the priority directions of the modern theory of gravity. Most of the exact solutions constructed within the framework of the general relativity are static or…
We analyze the conformal Einstein equation with a positive cosmological constant to extract fall-off conditions of the gravitational fields. The fall-off conditions are consistent with a finite, non-trivial presymplectic current on the…
Choptuik's critical phenomena in general relativity is revisited in the affine-null metric formulation of Einstein's equations for a massless scalar field in spherical symmetry. Numerical solutions are obtained by evolution of initial data…
We investigate five dimensional Einstein spaces in warped geometries from the point of view of the four dimensional physically relevant Robertson-Walker-Friedman cosmological metric and the Schwarzschild metric. We show that a…
We study the coupled Einstein-Klein-Gordon equations for a complex scalar field with and without a quartic self-interaction in a curvatureless Friedman-Lema\^{\i}\-tre Universe. The equations can be written as a set of four coupled first…
In this article, a special static spherically symmetric perfect fluid solution of Einstein's equations is provided. Though pressure and density both diverge at the origin, their ratio remains constant. The solution presented here fails to…
The confrontation between Einstein's gravitation theory and experimental results, notably binary pulsar data, is summarized and its significance discussed. Experiment and theory agree at the 10^{-3} level. All the basic structures of…
We study the spacelike Kasner singularity of spherically-symmetric, static and asymptotically flat black holes in Einstein gravity minimally coupled to a massless scalar with a suitable self-interacting scalar potential. We focus on how the…
We discuss new models of an `affine' theory of gravity in multidimensional space-times with symmetric connections. We use and develop ideas of Weyl, Eddington, and Einstein, in particular, Einstein's proposal to specify the space - time…
Bianchi VIII vacuum solutions to Einstein's equations are causally geodesically complete to the future, given an appropriate time orientation, and the objective of this article is to analyze the asymptotic behaviour of solutions in this…
This thesis is concerned with the development and application of conformal techniques to numerical calculations of asymptotically flat spacetimes. The conformal compactification technique enables us to calculate spatially unbounded domains,…
Asymptotic Safety (AS) Program for quantum gravity keeps the same fields and symmetries with General Relativity and studies the associated gravitational action as a fundamental part of the complete theory at the nonperturbative level with…
Static spherically symmetric solutions to the Einstein-Euler equations with prescribed central densities are known to exist, be unique and smooth for reasonable equations of state. Some criteria are also available to decide whether…
Although cosmological solutions to Einstein's equations are known to be generically singular, little is known about the nature of singularities in typical spacetimes. It is shown here how the operator splitting used in a particular…
Einstein's equations in matter are gravitational analogues of Maxwell's equations in matter, providing an effective classical description of gravitational fields. We derive Einstein's equations in matter for relativistic fluids, and use…
A recent proposal equates the circuit complexity of a quantum gravity state with the gravitational action of a certain patch of spacetime. Since Einstein's equations follow from varying the action, it should be possible to derive them by…
We discuss a number of topics in the area of conformally compact Einstein metrics, mostly centered around the global existence question of finding such metrics with an arbitrarily prescribed conformal infinity. The paper is partly a survey…
We analyze (the harmonic map representation of) static solutions of the Einstein Equations in dimension three from the point of view of comparison geometry. We find simple monotonic quantities capturing sharply the influence of the Lapse…
A discussion is given of the conformal Einstein field equations coupled with matter whose energy-momentum tensor is trace-free. These resulting equations are expressed in terms of a generic Weyl connection. The article shows how in the…