The linearized 3+1 TEGR system has imaginary eigenvalues in its principal symbol but becomes strongly hyperbolic after gauge fixing isolated problematic sectors.
A hyperbolic tetrad formulation of the Einstein equations for numerical relativity
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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.
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gr-qc 1years
2026 1verdicts
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Hyperbolicity analysis of the linearised 3+1 formulation in the Teleparallel Equivalent of General Relativity
The linearized 3+1 TEGR system has imaginary eigenvalues in its principal symbol but becomes strongly hyperbolic after gauge fixing isolated problematic sectors.