First-order symmetrizable hyperbolic formulations of Einstein's equations including lapse and shift as dynamical fields

TL;DR

This paper develops two first-order symmetrizable hyperbolic formulations of Einstein's equations that incorporate lapse and shift as dynamical fields, potentially improving numerical relativity simulations by avoiding elliptic solves.

Contribution

It introduces novel hyperbolic systems that treat lapse and shift as dynamical variables with physical characteristic speeds, unlike previous formulations.

Findings

Two new hyperbolic formulations including lapse and shift as dynamical fields.

Systems have only physical characteristic speeds.

Potential for more efficient numerical simulations of Einstein's equations.

Abstract

First-order hyperbolic systems are promising as a basis for numerical integration of Einstein's equations. In previous work, the lapse and shift have typically not been considered part of the hyperbolic system and have been prescribed independently. This can be expensive computationally, especially if the prescription involves solving elliptic equations. Therefore, including the lapse and shift in the hyperbolic system could be advantageous for numerical work. In this paper, two first-order symmetrizable hyperbolic systems are presented that include the lapse and shift as dynamical fields and have only physical characteristic speeds.