Numerical solutions to Einstein's equations in a shearing-dust Universe: a code comparison

Abstract

A number of codes for general-relativistic simulations of cosmological structure formation have been developed in recent years. Here we demonstrate that a sample of these codes produce consistent results beyond the Newtonian regime. We simulate solutions to Einstein's equations dominated by gravitomagnetism -- a vector-type gravitational field that doesn't exist in Newtonian gravity and produces frame-dragging, the leading-order post-Newtonian effect. We calculate the coordinate-invariant effect on intersecting null geodesics by performing ray tracing in each independent code. With this observable quantity, we assess and compare each code's ability to compute relativistic effects.

arXiv comment14 pages, 5 figures, accepted to CQG

References in corpus (75)

• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
• Measurements of Omega and Lambda from 42 High-Redshift Supernovae
• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters
• Dynamics of dark energy
• Modified Gravity and Cosmology
• Cosmological parameters from SDSS and WMAP
• LSST: from Science Drivers to Reference Design and Anticipated Data Products
• The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: cosmological analysis of the DR12 galaxy sample
• Cosmological Hydrodynamics with Adaptive Mesh Refinement: a new high resolution code called RAMSES
• Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics Beyond LambdaCDM
• Gravity Probe B: Final Results of a Space Experiment to Test General Relativity
• Dark Energy after GW170817: dead ends and the road ahead
• Everything You Always Wanted To Know About The Cosmological Constant Problem (But Were Afraid To Ask)
• Evolutions in 3D numerical relativity using fixed mesh refinement
• Planck evidence for a closed Universe and a possible crisis for cosmology
• The Einstein Toolkit: A Community Computational Infrastructure for Relativistic Astrophysics
• New Parallaxes of Galactic Cepheids from Spatially Scanning the Hubble Space Telescope: Implications for the Hubble Constant
• Dynamical dark energy in light of the latest observations
• Dark Energy vs. Modified Gravity
• Relativistic second-order perturbations of the Einstein-de Sitter Universe
• Non-minimal dark sector physics and cosmological tensions
• Science with the Square Kilometer Array: Motivation, Key Science Projects, Standards and Assumptions
• Perturbations of spacetime: gauge transformations and gauge invariance at second order and beyond
• Three-dimensional relativistic simulations of rotating neutron-star collapse to a Kerr black hole
• Indications of a late-time interaction in the dark sector
• Conformal and covariant formulation of the Z4 system with constraint-violation damping
• Galileon Gravity in Light of ISW, CMB, BAO and $H_0$ data
• A constrained scheme for Einstein equations based on Dirac gauge and spherical coordinates
• No evidence for extensions to the standard cosmological model
• Tension between the power spectrum of density perturbations measured on large and small scales
• General relativity and cosmic structure formation
• IllinoisGRMHD: An Open-Source, User-Friendly GRMHD Code for Dynamical Spacetimes
• gevolution: a cosmological N-body code based on General Relativity
• Model independent $H(z)$ reconstruction using the cosmic inverse distance ladder
• Observational Challenges for the Standard FLRW Model
• Constraints on the interacting vacuum -- geodesic CDM scenario
• Effects of nonlinear inhomogeneity on the cosmic expansion with numerical relativity
• Departures from the FLRW Cosmological Model in an Inhomogeneous Universe: A Numerical Examination
• An Introduction to the Einstein Toolkit
• Relativistic N-body simulations with massive neutrinos
• Computing General Relativistic effects from Newtonian N-body simulations: Frame dragging in the post-Friedmann approach
• Evolution of a periodic eight-black-hole lattice in numerical relativity
• Inhomogeneous Cosmology with Numerical Relativity
• Analysis of the doubly heavy baryon states and pentaquark states with QCD sum rules
• Einstein's Universe: Cosmological structure formation in numerical relativity
• Integration of inhomogeneous cosmological spacetimes in the BSSN formalism
• Post-$Planck$ constraints on interacting vacuum energy
• The cosmological background of vector modes
• Mathematical Issues in a Fully-Constrained Formulation of Einstein Equations
• Bias and scatter in the Hubble diagram from cosmological large-scale structure
• Observable Deviations from Homogeneity in an Inhomogeneous Universe
• The missing link: a nonlinear post-Friedmann framework for small and large scales
• Evolution of a family of expanding cubic black-hole lattices in numerical relativity
• The Generation of Vorticity in Cosmological N-body Simulations
• Safely smoothing spacetime: backreaction in relativistic cosmological simulations
• The trouble with Hubble: Local versus global expansion rates in inhomogeneous cosmological simulations with numerical relativity
• Comparing Fully General Relativistic and Newtonian Calculations of Structure Formation
• The effect of early radiation in N-body simulations of cosmic structure formation
• The Limited Accuracy of Linearized Gravity
• Light propagation through black-hole lattices
• Cosmic Censorship Upheld in Spheroidal Collapse of Collisionless Matter
• General Relativistic Corrections to the Weak Lensing Convergence Power Spectrum
• Cosmological backreaction within the Szekeres model and emergence of spatial curvature
• Gravitational waves in dynamical spacetimes with matter content in the Fully Constrained Formulation
• Cosmological nonlinear structure formation in full general relativity
• $f(R)$ gravity modifications: from the action to the data
• Distance-redshift relation in plane symmetric universes
• An automatically generated code for relativistic inhomogeneous cosmologies
• Lagrangian theory for cosmic structure formation with vorticity: Newtonian and post-Friedmann approximations
• Fully relativistic nonlinear cosmological evolution in spherical symmetry using the BSSN formalism
• GRAMSES: a new route to general relativistic $N$-body simulations in cosmology. Part II. Initial conditions
• Spherically Symmetric N-body Simulations with General Relativistic Dynamics
• Relativistic weak lensing from a fully non-linear cosmological density field
• Full-sky weak lensing: a nonlinear post-Friedmann treatment
• Observable cosmological vector mode in the dark ages

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• Weak-lensing observables in relativistic N-body simulations
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• $\text{Hi-COLA}$: Fast, approximate simulations of structure formation in Horndeski gravity
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