A hyperbolic tetrad formulation of the Einstein equations for numerical relativity

Abstract

The tetrad-based equations for vacuum gravity published by Estabrook, Robinson, and Wahlquist are simplified and adapted for numerical relativity. We show that the evolution equations as partial differential equations for the Ricci rotation coefficients constitute a rather simple first-order symmetrizable hyperbolic system, not only for the Nester gauge condition on the acceleration and angular velocity of the tetrad frames considered by Estabrook et al., but also for the Lorentz gauge condition of van Putten and Eardley, and for a fixed gauge condition. We introduce a lapse function and a shift vector to allow general coordinate evolution relative to the timelike congruence defined by the tetrad vector field.

Eqs. (59), (B3), (B4), and (B5) have been corrected (multiplied by -1). Two typos have been fixed, and citations have been removed from the abstract

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• Mathematical Structure of Tetrad Equations for Vacuum Relativity
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• A covariant Hamiltonian tetrad approach to numerical relativity
• Unveiling the electrodynamic nature of spacetime collisions
• A Note on the Strong Hyperbolicity of $f(R)$ Gravity with Dynamical Shifts
• First-order hyperbolic formulation of the pure tetrad teleparallel gravity theory
• On the nature of the new group LB1