First-Order Symmetric Hyperbolic Reductions of the EFE

  1. Friedrich H: On the Regular and the Asymptotic Characteristic Initial Value Problem for Einstein's Vacuum Field Equations, Proc. R. Soc. Lond. A 375 (1981), 169
    NB: Employs NP spin-frame formalism. The conformal Ricci scalar is treated as a gauge source function and is set to zero. Very technical. (+ - - -). Communicated by S W Hawking.
  2. Friedrich H: The Asymptotic Characteristic Initial Value Problem for Einstein's Vacuum Field Equations as an Initial Value Problem for a First-Order Quasilinear Symmetric Hyperbolic System, Proc. R. Soc. Lond. A 378 (1981), 401
    NB: Employs NP spin-frame formalism. The conformal Ricci scalar is treated as a gauge source function and is set to zero. Very technical. (+ - - -). Communicated by S W Hawking.
  3. Kind S, J Ehlers: Initial-Boundary Value Problem for the Spherically Symmetric Einstein Equations for a Perfect Fluid, Class. Quantum Grav. 10 (1993), 2123
    NB: Quite technical.
  4. Kind S, J Ehlers, B G Schmidt: Relativistic Stellar Oscillations Treated as an Initial Value Problem, Class. Quantum Grav. 10 (1993), 2137
    NB: Linearised perturbations of a star in hydrostatic equilibrium. Quite technical.
  5. Abrahams A, A Anderson, Y Choquet-Bruhat, J W York jr: Einstein and Yang-Mills Theories in Hyperbolic Form without Gauge-Fixing, Phys. Rev. Lett. 75 (1995), 3377
  6. Bona C, J Massó, E Seidel, J Stela: New Formalism for Numerical Relativity, Phys. Rev. Lett. 75 (1995), 600
    NB: Scheme is derived from the ADM 3+1 equations through introduction of auxiliary variables and explicit use of the momentum constraint and the gauge choice. Allows for a variety of invariant algebraic time slicing conditions such as "harmonic", "maximal" and "1+log". As such dependent on both choice of lapse and shift.
  7. Friedrich H: Hyperbolic Reductions for Einstein's Equations, Class. Quantum Grav. 13 (1996), 1451
    NB: The second Bianchi identity is at the heart of the two formulations provided: one based on an ONF scheme, the other on a ADM 3+1 picture. Discusses in detail the concept of gauge source functions. A modification of the "harmonic" time slicing condition yields the gauge specification. Treats the vacuum EFE case only.
  8. Frittelli S, O A Reula: First Order Symmetric Hyperbolic Einstein Equations with Arbitrary Fixed Gauge, Phys. Rev. Lett. 76 (1996), 4667
  9. Geroch R: Partial Differential Equations of Physics, in General Relativity (Proc. 46th Scottish Universities Summer School in Physics), Eds. G S Hall and J R Pulham (Edinburgh: SUSSP Publications, London: IOP Publishing, 1996). Also: Preprint gr-qc/9602055.
  10. van Putten M H P M, D M Eardley: Nonlinear Wave Equations for Relativity, Phys. Rev. D 53 (1996), 3056
  11. Abrahams A, A Anderson, Y Choquet-Bruhat, J W York jr: Geometrical Hyperbolic Systems for General Relativity and Gauge Theories, Class. Quantum Grav. 14 (1997), A9
    NB: Scheme is based on derivatives of the ADM 3+1 equations. Spatially covariant in that it is shift-independent, but restricted to a generalised "harmonic" time slicing condition only. Mainly deals with the vacuum EFE case.
  12. Estabrook F B, R S Robinson, H D Wahlquist: Hyperbolic Equations for Vacuum Gravity Using Special Orthonormal Frames, Class. Quantum Grav. 14 (1997), 1237
  13. Friedrich H: Evolution Equations for Gravitating Ideal Fluid Bodies in General Relativity, Phys. Rev. D 57 (1998), 2317
  14. Reula O A: Hyperbolic Methods for Einstein's Equations, Max-Planck-Gesellschaft Living Reviews Series, No. 1998-3
  15. Stewart J M: The Cauchy Problem and the Initial Boundary Value Problem in Numerical Relativity, Class. Quantum Grav. 15 (1998), 2865
  16. van Elst H, G F R Ellis: Causal Propagation of Geometrical Fields in Relativistic Cosmology, Phys. Rev. D 59 (1999), 024013. Also: Preprint gr-qc/9810058.
  17. van Elst H, G F R Ellis, B G Schmidt: On the Propagation of Jump Discontinuities in Relativistic Cosmology, Preprint gr-qc/0007003, uct-cosmology-00/06, AEI-2000-039
  18. Friedrich H, A D Rendall: The Cauchy Problem for the Einstein Equations, in Einstein's Field Equations and their Physical Interpretation, ed. B G Schmidt, (Berlin: Springer, 2000), 127. Also: Preprint gr-qc/0002074, AEI-2000-012.

Selected References
Last revision: Tue, 15-8-2000 (This page is under construction)