TL;DR
Numerical Relativity combines physics and computational techniques to simulate complex, dynamic gravitational phenomena, focusing on solving Einstein's equations for strong gravity scenarios where approximations fail.
Contribution
This paper introduces the foundational concepts, formalisms, and numerical methods used in Numerical Relativity for modeling gravitational wave sources.
Findings
Formulation of Einstein equations as well-posed evolution systems
Overview of formalisms and coordinate choices in Numerical Relativity
Discussion of numerical methods for simulating gravitational dynamics
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.
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