Related papers: Numerical Integration of Nonlinear Wave Equations …
Axisymmetric numerical simulations of rotating stellar core collapse to a neutron star are performed in the framework of full general relativity. The so-called Cartoon method, in which the Einstein field equations are solved in the…
We present a new approach for achieving high-order convergence in fully general-relativistic hydrodynamic simulations. The approach is implemented in WhiskyTHC, a new code that makes use of state-of-the-art numerical schemes and was key in…
We present a new method of extracting gravitational radiation from three-dimensional numerical relativity codes and providing outer boundary conditions. Our approach matches the solution of a Cauchy evolution of Einstein's equations to a…
The Cosmological Gravitational Wave Background (CGWB) anisotropies contain valuable information about the physics of the early universe. Given that General Relativity is intrinsically nonlinear, it is important to look beyond first-order…
We study Einstein's equations with matter in hydrostatic equilibrium in the nonstandard gauge which was recently investigated in the vacuum case. We obtain spherically symmetric solutions for any given rotation curve. These solutions can be…
Nonlinear evolution equations of the fourth order and its partial cases are derived for describing nonlinear pressure waves in a mixture liquid and gas bubbles. Influence of viscosity and heat transfer is taken into account. Exact solutions…
Cosmological perturbation theory is a key tool to study the universe. The linear or first order theory is well understood, however, developing and applying the theory beyond linear order is at the cutting edge of current research in…
Gravitational waves (GWs) from merging black holes allow for unprecedented probes of strong-field gravity. Testing gravity in this regime requires accurate predictions of gravitational waveform templates in viable extensions of General…
This work is to study the generalized second law (GSL) of thermodynamics in tachyon cosmology where the boundary of the universe is assumed to be enclosed by a dynamical apparent horizon. The model is constrained with the observational…
We are interested in coupled semi-linear wave equations satisfying the null condition in two space dimensions, a basic model in nonlinear wave equations. Our aim is to establish global existence of smooth solutions to this system with large…
General relativity describes the dynamics of gravitational waves, which can feature nonlinear interactions, such as those underlying turbulent processes. Theoretical and numerical explorations have demonstrated the existence of…
In a recent paper (Beyer and Hennig, 2012 [9]), we have introduced a class of inhomogeneous cosmological models: the smooth Gowdy-symmetric generalized Taub-NUT solutions. Here we derive a three-parametric family of exact solutions within…
We are developing 3 dimensional simulation codes for coalescing binary neutron stars. A code using the maximal slicing condition is obtained. To evaluate the gravitational radiation, we implemented a gauge-invariant wave extraction and…
This work reports on the construction of a nonlinear distributional geometry (in the sense of Colombeau's special setting) and its applications to general relativity with a special focus on the distributional description of impulsive…
We study a space-time finite element approach for the nonhomogeneous wave equation using a continuous time Galerkin method. We present fully implicit examples in 1+1, 2+1, and 3+1 dimensions using linear quadrilateral, hexahedral, and…
This article is concerned with infinite depth gravity water waves in two space dimensions. We consider this system expressed in position-velocity potential holomorphic coordinates. Our goal is to study this problem with small wave packet…
Second-order tensor modes induced by nonlinear gravity are a key component of the cosmological background of gravitational waves. A detection of this background would allow us to probe the primordial power spectrum at otherwise inaccessible…
We give a comprehensive analysis of interrelations between the basic concepts of the modern theory of symmetry (classical and non-classical) reductions of partial differential equations. Using the introduced definition of reduction of…
We present an elementary method to obtain the equations of the shallow-water solitary waves in different orders of approximation. The first two of these equations are solved to get the shapes and propagation velocities of the corresponding…
We use covariant and first-order formalism techniques to study the properties of general relativistic cosmology in three dimensions. The covariant approach provides an irreducible decomposition of the relativistic equations, which allows…