Related papers: Numerical Relativity in 3+1 Dimensions
We review recent efforts to re-formulate the Einstein equations for fully relativistic numerical simulations. The so-called numerical relativity (computational simulations in general relativity) is a promising research field matching with…
This article begins with a brief introduction to numerical relativity aimed at readers who have a background in applied mathematics but not necessarily in general relativity. I then introduce and summarise my work on the problem of treating…
We present a model of non-relativistic gravitational theory which is power-counting renormalizable in 3+1 dimensional spacetime. When applied to cosmology, the relativity-violation terms lead to a dark radiation component, which can give…
The generalized harmonic equations of general relativity are written in 3+1 form. The result is a system of partial differential equations with first order time and second order space derivatives for the spatial metric, extrinsic curvature,…
A new numerical scheme to solve the Einstein field equations based upon the generalized harmonic decomposition of the Ricci tensor is introduced. The source functions driving the wave equations that define generalized harmonic coordinates…
We demonstrate that evolutions of three-dimensional, strongly non-linear gravitational waves can be followed in numerical relativity, hence allowing many interesting studies of both fundamental and observational consequences. We study the…
Gravitational waves deliver information in exquisite detail about astrophysical phenomena, among them the collision of two black holes, a system completely invisible to the eyes of electromagnetic telescopes. Models that predict…
General exact solution is obtained for the problem of the development of arbitrary disturbances of the density and velocity in a (1+1)-dimensional universe. This analytical solution may serve, particularly, as a test for numerical methods.…
We report on a systematic study of the dynamics of gravitational waves in full 3D numerical relativity. We find that there exists an interesting regime in the parameter space of the wave configurations: a near-linear regime in which the…
Numerical-relativity (NR) simulations of compact binaries are expected to be an invaluable tool in gravitational-wave (GW) astronomy. The sensitivity of future detectors such as the Einstein Telescope (ET) will place much higher demands on…
In three spacetime dimensions, general relativity becomes a topological field theory, whose dynamics can be largely described holographically by a two-dimensional conformal field theory at the ``boundary'' of spacetime. I review what is…
The extreme-gravity collisions of binaries with one black hole and one neutron star provide for excellent tests of general relativity. We here study how well one can constrain theories beyond general relativity with additional scalar fields…
The numerical relativity session at GR18 was dominated by physics results on binary black hole mergers. Several groups can now simulate these from a time when the post-Newtonian equations of motion are still applicable, through several…
A code that implements Einstein equations in the characteristic formulation in 3D has been developed and thoroughly tested for the vacuum case. Here, we describe how to incorporate matter, in the form of a perfect fluid, into the code. The…
Spherically symmetric (1D) black-hole spacetimes are considered as a test for numerical relativity. A finite difference code, based in the hyperbolic structure of Einstein's equations with the harmonic slicing condition is presented.…
In this work numerical methods for solving Einstein's equations are developed and applied to the study of inhomogeneous cosmological models. A two-dimensional computer code is described which implements two advanced numerical methods:…
Some exact static solutions for Einstein gravity in 2+1 dimensions coupled to abelian gauge field are discussed. Some of these solutions are three-dimensional analogs of the Schwarzschild black holes. The metrics in the regions inside and…
We model two mergers of orbiting binary neutron stars, the first forming a black hole and the second a differentially rotating neutron star. We extract gravitational waveforms in the wave zone. Comparisons to a post-Newtonian analysis allow…
Using the (3+1) formalism in general relativity, we perform the post-Newtonian(PN) approximation to clarify what sort of gauge condition is suitable for numerical analysis of coalescing compact binary neutron stars and gravitational waves…
Black holes are popping up all over the place: in compact binary X-ray sources and GRBs, in quasars, AGNs and the cores of all bulge galaxies, in binary black holes and binary black hole-neutron stars, and maybe even in the LHC! Black holes…