Related papers: High-frequency solutions to the constraint equatio…
In this paper, we present a framework for getting a series of exact vacuum solutions to the Einstein equation. This procedure of resolution is based on a canonical form of the metric. According to this procedure, the Einstein equation can…
We investigate how the accuracy and stability of numerical relativity simulations of 1D colliding plane waves depends on choices of equation formulations, gauge conditions, boundary conditions, and numerical methods, all in the context of a…
The collision of two plane gravitational waves in Einstein's theory of relativity can be described mathematically by a Goursat problem for the hyperbolic Ernst equation in a triangular domain. We use the integrable structure of the Ernst…
New boundary conditions are imposed on the familiar cylindrical gravitational wave vacuum spacetimes. The new spacetime family represents cylindrical waves in a flat expanding (Kasner) universe. Space sections are flat and nonconical where…
We compute families of solutions to the Einstein vacuum equations of the type of Brill waves, but with slow fall-off towards spatial infinity. We prove existence and uniqueness of solutions for physical data and numerically construct some…
A generalized geometric method is developed for constructing exact solutions of gravitational field equations in Einstein theory and generalizations. First, we apply the formalism of nonholonomic frame deformations (formally considered for…
A proper-time method for constructing models of dynamic gravitational-wave fields is presented. Using the proper-time method, analytical (not numerical) models of secondary gravitational waves are constructed as perturbative solutions of…
A nonstatic and circularly symmetric exact solution of the Einstein equations (with a cosmological constant $\Lambda$ and null fluid) in $2+1$ dimensions is given. This is a nonstatic generalization of the uncharged spinless BTZ metric. For…
The almost scale-invariant spectrum for the stochastic background wave (in primordial Universe) is a firm prediction of inflationary scenarios. In the present work, to study of primordial Gravitational Waves, one dimensional toy model in…
We analyze existence and properties of solutions of two-dimensional general relativistic initial data sets with a negative cosmological constant, both on spacelike and characteristic surfaces. A new family of such vacuum, spacelike data…
This paper concerns the construction and analysis of a new family of exact general relativistic shock waves. The construction resolves the open problem of determining the expanding waves created behind a shock-wave explosion into a static…
We perform an optimal localization of asymptotically flat initial data sets and construct data that have positive ADM mass but are exactly trivial outside a cone of arbitrarily small aperture. The gluing scheme that we develop allows to…
A new class of exact solutions of Einstein's field equations with a perfect fluid source, variable gravitational coupling $G$ and cosmological term $\Lambda$ for FRW spacetime is obtained by considering variable deceleration parameter…
The models of New General Relativity have recently got attention of research community, and there are some works studying their dynamical properties. The formal aspects of this investigation have been mostly restricted to the primary…
A review of the treatment of boundaries in general relativity is presented with the emphasis on application to the formulations of Einstein's equations used in numerical relativity. At present, it is known how to treat boundaries in the…
Gravitational waves are investigated in Intrinsic Time Geometrodynamics. This theory has a non-vanishing physical Hamiltonian generating intrinsic time development in our expanding universe, and four-covariance is explicitly broken by…
We prove global stability of Minkowski space for the Einstein vacuum equations in harmonic (wave) coordinate gauge for the set of restricted data coinciding with Schwartzschild solution in the neighborhood of space-like infinity. The result…
Let $( \bar g, \bar k)$ be a solution to the maximal constraint equations of general relativity on the unit ball $B_1$ of $\mathbb{R}^3$. We prove that if $(\bar g,\bar k)$ is sufficiently close to the initial data for Minkowski space, then…
We use the mathematical framework of loop quantum gravity (LQG) to study the quantization of three dimensional (Riemannian) gravity with positive cosmological constant (Lambda>0). We show that the usual regularization techniques (successful…
Gravitational waves offer a potent mean to test the underlying theory of gravity. In general theories of gravity, such as scalar-tensor theories, one expects modifications in the friction term and the sound speed in the gravitational wave…