Related papers: Fixed mesh refinement in the characteristic formul…
This paper considers a numerical solution of a linear elasticity problem, namely the Cauchy-Navier equation, using a strong form method based on a local Weighted Least Squares (WLS) approximation. The main advantage of the employed…
In general relativity, perturbation theory about a background solution fails if the background spacetime has a Killing symmetry and a compact spacelike Cauchy surface. This failure, dubbed as {\it linearization instability}, shows itself as…
The Cold Dark Matter (CDM) model, wherein the dark matter is treated as a pressureless perfect fluid, provides a good fit to galactic and cosmological data. With the advent of precision cosmology, it should be asked whether this simplest…
This article investigates residual a posteriori error estimates and adaptive mesh refinements for time-dependent boundary element methods for the wave equation. We obtain reliable estimates for Dirichlet and acoustic boundary conditions…
We show that it is possible to steer clear of a spacetime singularity during gravitational collapse by considering the time-variation of a fundamental coupling, in this case, the fine structure constant {\alpha}. We study a spherical…
Stochastic models of chemical systems are often analysed by solving the corresponding Fokker-Planck equation which is a drift-diffusion partial differential equation for the probability distribution function. Efficient numerical solution of…
In a Lorentzian spacetime there exists a smooth regular line element field $(\bm{X},-\bm{X}) $ and a unit vector $ \bm{u} $ collinear with one of the pair of vectors in the line element field. An orthogonal decomposition of symmetric…
The precise tuning required to observe critical phenomena in gravitational collapse poses a challenge for most numerical codes. First, threshold estimation searches may be obstructed by the appearance of coordinate singularities, indicating…
For a large class of scalar-tensor-like modified gravity whose action contains nonminimal couplings between a scalar field $\phi(x^\alpha)$ and generic curvature invariants $\mathcal{R}$ beyond the Ricci scalar $R=R^\alpha_{\;\;\alpha}$, we…
In General Relativity approximations based on the spherical collapse model such as Press--Schechter theory and its extensions are able to predict the number of objects of a certain mass in a given volume. In this paper we use a machine…
Along with the construction of non-Lorentz-invariant effective field theories, recent studies which are based on geometric models of Finsler space-time become more and more popular. In this respect, the Finslerian approach to the problem of…
We present an analytical description of the probability distribution function (PDF) of the smoothed three-dimensional matter density field for modified gravity and dark energy. Our approach, based on the principles of Large Deviations…
We propose an action-based $ f(R) $ modification of Einstein's gravity which admits of a modified Schwarzschild-deSitter metric. In the weak field limit this amounts to adding a small logarithmic correction to the newtonian potential. A…
In extensions of general relativity and in theories aiming at unifying gravity with the forces of the Standard Model, the value of the "fundamental constants" is often determined by the vacuum expectation value of new fields, which may thus…
The characteristic formalism of numerical relativity is based on a system of coordinates aligned with outgoing null cones. While these coordinates were designed for studying gravitational waves, they can also be easily adapted to model…
Within the framework of metric-affine gravity (MAG, metric and an independent linear connection constitute spacetime), we find, for a specific gravitational Lagrangian and by using {\it prolongation} techniques, a stationary axially…
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…
We employ Maxwell's equations formulated in Space-Time Algebra to perform discretization of moving geometries directly in space-time. All the derivations are carried out without any non-relativistic assumptions, thus the application area of…
We present here the linear regime of the Einstein's field equations in the characteristic formulation. Through a simple decomposition of the metric variables in spin-weighted spherical harmonics, the field equations are expressed as a…
General relativity is a non-linear theory with the distinguishing feature that gravitational field energy also acts as gravitational charge density. In the well-known Schwarzschild solution describing field of an isolated massive body at…