Introduction to Numerical Relativity

Abstract

Numerical Relativity is a multidisciplinary field including relativity, magneto-hydrodynamics, astrophysics and computational methods, among others, with the aim of solving numerically highly-dynamical, strong-gravity scenarios where no other approximations are available. Here we describe some of the foundations of the field, starting from the covariant Einstein equations and how to write them as a well-posed system of evolution equations, discussing the different formalisms, coordinate conditions and numerical methods commonly employed nowadays for the modeling of gravitational wave sources.

Accepted by Frontiers Astronomy and Space Sciences, invited review for the Research Topic "Gravitational Waves: A New Window to the Universe"

References in corpus (14)

• The Confrontation between General Relativity and Experiment
• Calibration of Moving Puncture Simulations
• Accurate evolutions of inspiralling neutron-star binaries: prompt and delayed collapse to black hole
• Binary black hole merger dynamics and waveforms
• How to move a black hole without excision: gauge conditions for the numerical evolution of a moving puncture
• Simulating coalescing compact binaries by a new code SACRA
• General relativistic simulations of magnetized binary neutron star mergers
• Binary black-hole evolutions of excision and puncture data
• Simulation of Binary Black Hole Spacetimes with a Harmonic Evolution Scheme
• Head-on collisions of boson stars
• The last orbit of binary black holes
• Simulating binary neutron stars: dynamics and gravitational waves
• Well-posedness of formulations of the Einstein equations with dynamical lapse and shift conditions
• Action principle for Numerical Relativity evolution systems