Related papers: Numerical Relativity in Spherical Polar Coordinate…
While the use of numerical general relativity for modeling astrophysical phenomena and compact objects is commonplace, the application to cosmological scenarios is only just beginning. Here, we examine the expansion of a spacetime using the…
The puncture method for dealing with black holes in the numerical simulation of vacuum spacetimes is remarkably successful when combined with the BSSN formulation of the Einstein equations. We examine a generalized class of formulations…
Numerical relativity has traditionally been pursued via finite differencing. Here we explore pseudospectral collocation (PSC) as an alternative to finite differencing, focusing particularly on the solution of the Hamiltonian constraint (an…
We present numerical results and computer assisted proofs of the existence of periodic orbits for the Kuramoto-Sivashinky equation. These two results are based on writing down the existence of periodic orbits as zeros of functionals. This…
We present a code for solving the nonlinear force-free equations in spherical polar geometry, with the motivation of modeling the magnetic field in the corona. The code is an implementation of the Grad-Rubin method. Our method is applicable…
We investigate the conditions under which cosmological variations in physical `constants' and scalar fields are detectable on the surface of local gravitationally-bound systems, such as planets, in non-spherically symmetric background…
One of the most promising sources of gravitational radiation is coalescence of binary neutron stars or black holes. In order to study gravitational radiation at the merging phase of coalescing binary neutron stars which is called the last…
The paper presents equations determining the particle spin evolution in the post-Newtonian approximation in the problem of motion of two mass and spin possessing particles. The equations are derived with the Einstein-Infeld-Hoffmann method…
Different formulations of Einstein's equations used in numerical relativity can affect not only the stability but also the accuracy of numerical simulations. In the original Baumgarte-Shapiro-Shibata-Nakamura (BSSN) formulation, the loss of…
Static coordinates can be convenient to solve the vacuum Einstein's equations in presence of spherical symmetry, but for cosmological applications comoving coordinates are more suitable to describe an expanding Universe, especially in the…
The development of hyperbolic formulations of Einstein's equations has revolutionized our ability to perform long-time, stable, accurate numerical simulations of strong field gravitational phenomena. However, hyperbolic methods have seen…
A new evolution algorithm for the characteristic initial value problem based upon an affine parameter rather than the areal radial coordinate used in the Bondi-Sachs formulation is applied in the spherically symmetric case to the…
We study propagation of high-frequency electromagnetic waves in a curved spacetime. We demonstrate how a modification of the standard geometric optics allows one to include the helicity dependent corrections into the equations of motion of…
We survey many of the important properties of spherically symmetric spacetimes as follows. We present several different ways of describing a spherically symmetric spacetime and the resulting metrics. We then focus our discussion on an…
We present numerical solutions of the hyperboloidal initial value problem for a self-gravitating scalar field in spherical symmetry, using a variety of standard hyperbolic slicing and shift conditions that we adapt to our hyperboloidal…
We propose a novel statistical method to measure cosmic birefringence and demonstrate its power in probing parity violation due to axions. Exploiting an empirical correlation between the integrated radio polarization direction of a spiral…
Numerical integration on spheres, including the computation of the areas of spherical triangles, is a core computation in geomathematics. The commonly used techniques sometimes suffer from instabilities and significant loss of accuracy. We…
Possible violations of fundamental physical principles, e.g. the Einstein equivalence prin- ciple on which all metric theories of gravity are based, including general relativity (GR), would lead to a rotation of the plane of polarization…
We present a new numerical relativity code designed for simulations of compact binaries involving matter. The code is an upgrade of the BAM code to include general relativistic hydrodynamics and implements state-of-the-art…
The numerical evolution of Einstein's field equations in a generic background has the potential to answer a variety of important questions in physics: from applications to the gauge-gravity duality, to modelling black hole production in TeV…