Related papers: Cauchy-characteristic matching
Vacuum solutions to the Einstein equations can be viewed as the interplay between the geometry and the gravitational wave energy content. The constraints on initial data reflect this interaction. We assume we are looking at cosmological…
It is formulated a new 'anholonomic frame' method of constructing exact solutions of Einstein equations with off--diagonal metrics in 4D and 5D gravity. The previous approaches and results are summarized and generalized as three theorems…
The Einstein-Vlasov-Fokker-Planck system describes the kinetic diffusion dynamics of self-gravitating particles within the Einstein theory of general relativity. We study the Cauchy problem for spatially homogeneous and isotropic solutions…
I review recent developments in numerical relativity, focussing on progress made in 3D black hole evolution. Progress in development of black hole initial data, apparent horizon boundary conditions, adaptive mesh refinement, and…
We study the three dimensional Einstein gravity conformally coupled to a scalar field. Solutions of this theory are geometries with vanishing scalar curvature. We consider solutions with a constant scalar field which corresponds to an…
In this work, in the context of modified gravity, a curved spacetime analogous to the "canonical acoustic black hole" is constructed. The source is a self-interacting scalar field which is non-minimally coupled to gravity through the…
We show that the maximal globally hyperbolic solution of the initial-value problem for the higher-dimensional vacuum Einstein equations on two transversally intersecting characteristic hypersurfaces contains a future neighborhood of the…
We study the Cauchy problem of higher dimensional Einstein-Maxwell-Higgs system in the framework of Bondi coordinates. As a first step, the problem is reduced to a single first-order integro-differential equation by defining a generalized…
We investigate the numerical stability of Cauchy evolution of linearized gravitational theory in a 3-dimensional bounded domain. Criteria of robust stability are proposed, developed into a testbed and used to study various…
We present an introduction to dynamical trapping horizons as quasi-local models for black hole horizons, from the perspective of an Initial Value Problem approach to the construction of generic black hole spacetimes. We focus on the…
Deriving the gravitational effective action directly from exact renormalization group is very complicated, if not impossible. Hence, to study the effects of running gravitational coupling which tends to a non--Gaussian UV fixed point (as it…
Gauge-gravity duality is arguably our best hope for understanding quantum gravity. Considerable progress has been made in relating scattering amplitudes in certain gravity theories to those in gauge theories---a correspondence dubbed the…
We present a framework to propagate to null infinity gravitational waves computed at timelike worldtubes in the interior of a 3+1 (Cauchy) numerical relativity simulations. In our method, numerical relativity data are used as the inner…
The Einstein evolution equations are studied in a gauge given by a combination of the constant mean curvature and spatial harmonic coordinate conditions. This leads to a coupled quasilinear elliptic--hyperbolic system of evolution…
A new principle in quantum gravity, dubbed spacetime complexity, states that gravitational physics emerges from spacetime seeking to optimize the computational cost of its quantum dynamics. Thus far, this principle has been realized at the…
Astrophysical black hole candidates, although long thought to have a horizon, could be horizonless ultra-compact objects. This intriguing possibility is motivated by the black hole information paradox and a plausible fundamental connection…
The article presents a series of numerical simulations of exact solutions of the Einstein equations performed using the Cactus code, a complete 3-dimensional machinery for numerical relativity. We describe an application (``thorn'') for the…
A solution for the Einstein gravity coupled with non linear electrodynamics is introduced in 2+1 dimensions. Especially, in the case with a non-vanishing cosmological constant, we obtain a novel black hole solution. To find fundamental…
All black holes (BHs) in nature are expected to be described by the Kerr vacuum solution of general relativity (GR). However, the Kerr BH interior contains several problematic features such as a Cauchy horizon, a curvature singularity, and…
This work is on the Cauchy problem for critical wave maps coupled to Einstein's equations of general relativity. The main result of this work is the proof that the energy of the Einstein-equivariant wave map system does not concentrate…