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The non-linear stability of the sub-extremal Schwarzschild-de Sitter spacetime in the stationary region near the conformal boundary is analysed using a technique based on the extended conformal Einstein field equations and a conformal…
The gravitational wave solutions obtained from a perturbation about conformally flat backgrounds in Einstein gravity are investigated. A perturbation theory analysis of the Lesame, Ellis and Dunsby results, based on a covariant approach,…
The paper is devoted to investigating long time behavior of smooth small data solutions to 3-D quasilinear wave equations outside of compact convex obstacles with Neumann boundary conditions.
A rarely exploited advantage of time-domain boundary integral equations compared to their frequency counterparts is that they can be used to treat certain nonlinear problems. In this work we investigate the scattering of acoustic waves by a…
In this paper, we give a criterion on the Cauchy data for the semilinear wave equations satisfying the null condition in $\mathbb{R}^+\times\mathbb{R}^{3}$ such that the energy of the data can be arbitrarily large while the solution is…
We construct exact solutions to the Bianchi equations on a flat spacetime background. When the constraints are satisfied, these solutions represent in- and outgoing linearized gravitational radiation. We then consider the Bianchi equations…
I review the development of numerical evolution codes for general relativity based upon the characteristic initial value problem. Progress is traced from the early stage of 1D feasibility studies to 2D axisymmetric codes that accurately…
We introduce a new wave formulation for the relativistic Euler equations with vacuum boundary conditions that consists of a system of non-linear wave equations in divergence form with a combination of acoustic and Dirichlet boundary…
We undertake a systematic review of some results concerning local well-posedness of the Cauchy problem for certain systems of nonlinear wave equations, with minimal regularity assumptions on the initial data. Moreover we provide a…
Numerical simulation of evolution of a cluster of a finite number of gravitating bodies interacting only by their intrinsic gravity has been carried out. The goal of the study was to reveal the main characteristic phases of the spatial…
We develop a general framework for effective equations of expectation values in quantum cosmology and pose for them the quantum Cauchy problem with no-boundary and tunneling wavefunctions. We apply this framework in the model with a big…
This study revisits the problem of identifying the unknown interior Robin boundary of a connected domain using Cauchy data from the exterior region of a harmonic function. It investigates two shape optimization reformulations employing…
In this paper, we study the Cauchy problem for a nonlinear wave equation with frictional and viscoelastic damping terms. Our aim is to obtain the threshold, to classify the global existence of solution for small data or the finite time…
The paper presents results for deriving closed-form analytic solutions of the non-relativistic linear perturbation equations, which govern the evolution of inhomogeneities in a homogeneous spatially flat multicomponent cosmological model.…
We study the following problem: Given initial data on a compact Cauchy horizon, does there exist a unique solution to wave equations on the globally hyperbolic region? Our main results apply to any spacetime satisfying the null energy…
We study the Cauchy problem for 3-D nonlinear elastic waves satisfying the null condition with low regularity initial data. In the radially symmetric case, we prove the global existence of a low regularity solution for every small data in…
The hypothesis of an alternative way of obtaining gravitational waves is the physical motivation of this article. Using the linear field approximation and a symmetry transformation of the affine connection, new field equations and new gauge…
We consider gravitational field equations which are Einstein equations written in terms of embedding coordinates in some higher dimensional Minkowski space. Our main focus is to address some tricky issues relating to the Cauchy problem and…
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 prove the existence of global solutions to the Cauchy problem for noncommutative nonlinear wave equations in arbitrary even spatial dimensions where the noncommutativity is only in the spatial directions. We find that for existence there…