Exploiting analogies between gravity and electrodynamics for numerical relativity

General relativity and electrodynamics are both governed by systems of hyperbolic equations which need to satisfy a set of elliptic constraints throughout evolution. Approaches to solve numerically the Maxwell equations in the presence of charges has led to a variety of advantageous techniques developed over decades, such as particle-in-cell (N-body) simulations, unstructured meshes and machine-precision constraint-preserving discretizations.

However, these and other techniques appear much more complicated to implement for numerical relativity. In this talk we will explore analogies between the Einstein and Maxwell systems that could allow numerical relativity to benefit from some of the techniques originally developed for numerical electrodynamics and plasma physics.

These could also offer an alternative, yet intuitive, insight into spacetime dynamics. Finally, we will discuss some of the challenges that need to be overcome for an effective numerical implementation.