Solving the Einstein Equations Numerically

TL;DR

Numerical relativity is essential for computing dynamical spacetimes in general relativity, involving initial value formulations, computational methods, and ongoing development of 3D codes.

Contribution

This paper provides an overview of numerical relativity, including formulation choices, fundamental concepts, and current computational tools, highlighting recent advances.

Findings

Discussion of initial value problem formulation

Review of standard numerical methods

Overview of active 3D codes

Abstract

There are many complementary approaches to the construction of solutions to the field equations of general relativity. Among these, numerical approximation offers the only possibility to compute a variety of dynamical spacetimes, and so has come to play an important role for theory and experiment alike. Presently we give a brief introduction to this, the science of numerical relativity. We discuss the freedom in formulating general relativity as an initial (boundary) value problem. We touch on the fundamental concepts of well-posedness and gauge freedom and review the standard computational methods employed in the field. We discuss the physical interpretation of numerical spacetime data and end with an overview of a number of 3d codes that are either in use or under active development.