Numerical Relativity

  1. Choptuik M W, D S Goldwirth, T Piran: A Direct Comparison of Two Codes in Numerical Relativity, Class. Quantum Grav. 9 (1992), 721
    NB: Minimally coupled massless scalar field in spherically symmetric spacetime; characteristic vs ADM $3+1$ Cauchy formulation.
  2. Gourgoulhon E: 1D Numerical Relativity Applied to Neutron Star Collapse, Class. Quantum Grav. 9 (1992), S117
  3. Lanza A: Multigrid in General Relativity: II. Kerr Spacetime, Class. Quantum Grav. 9 (1992), 677
  4. Bishop N T: Numerical Relativity: Combining the Cauchy and Characteristic Initial Value Problems, Class. Quantum Grav. 10 (1993), 333
    NB: Discussion given on the basis of a non-rotating axially symmetric geometry.
  5. Choptuik M W: Universality and Scaling in Gravitational Collapse of a Massless Scalar Field, Phys. Rev. Lett. 70 (1993), 9
  6. Frauendiener J, B G Schmidt: Numerical Evolution, Linear and Nonlinear, of Spherically Symmetric Deviations from an Isotropic Universe, Gen. Rel. Grav. 25 (1993), 373
    NB: Spherically symmetric deviations from a $k = 0$ radiation FLRW model. $1+1$-dependent equation system in FOSH form as a basis (cf. Kind/Ehlers `93).
  7. Clarke C J S, R A d'Inverno: Combining Cauchy and Characteristic Numerical Evolutions in Curved Coordinates, Class. Quantum Grav. 11 (1994), 1463
  8. Salisbury D C et al: A Connection Approach to Numerical Relativity, Class. Quantum Grav. 11 (1994), 2789
    NB: Ashtekar connection and NP conformal scalars providing dynamical variables.
  9. Seidel E, W-M Suen: Numerical Relativity, Int. J. Mod. Phys. C (1994)
  10. Berger B K, D Garfinkle, V Swamy: Detection of Computer Generated Gravitational Waves in Numerical Cosmologies, Gen. Rel. Grav. 27 (1995), 511. Also: Preprint gr-qc/9405069.
    NB: Geodesic motion of test particles in the plane symmetric ($G_{2}$) vacuum Gowdy model of $T^{3}\times R$ topology.
  11. Gunnarsen L, H-A Shinkai, K-I Maeda: A `3+1' Method for Finding Principal Null Directions, Class. Quantum Grav. 12 (1995), 133
    NB: Example discussed: Kastor-Traschen spacetimes.
  12. Romano J D, R H Price: Embedding Initial Data for Black-Hole Collisions, Class. Quantum Grav. 12 (1995), 875
  13. Balakrishna J, G Daues, E Seidel, W-M Suen, M Tobias, E Wang: Coordinate Conditions in Three-Dimensional Numerical Relativity, Class. Quantum Grav. 13 (1996), L135. Also: Preprint gr-qc/9601027.
  14. Hamadé R S, J M Stewart: The Spherically Symmetric Collapse of a Massless Scalar Field, Class. Quantum Grav. 13 (1996), 497. Also: Preprint gr-qc/9506044.
  15. Seidel E: Numerical Relativity and Black-Hole Collisions, in Relativity and Scientific Computing, Eds. F W Hehl, R A Puntigam, H Ruder, (Berlin: Springer-Verlag, 1996)
  16. Berger B K, D Garfinkle, E Strasser: New Algorithm for Mixmaster Dynamics, Class. Quantum Grav. 14 (1997), L29. Also: Preprint gr-qc/9609072.
  17. Gómez R, L Lehner, P Papadopoulos, J Winicour: The $e$th Formalism in Numerical Relativity, Class. Quantum Grav. 14 (1997), 977
    NB: Employing two overlapping stereographic coordinate patches to avoid the polar singularities of spherical coordinates.
  18. Gundlach C, J Pullin: Ill-Posedness of a Double-Null Free-Evolution Scheme for Black Hole Spacetimes, Class. Quantum Grav. 14 (1997), 991. Also: Preprint gr-qc/9606022.
    NB: Double-null methods may contain exponentially growing non-physical modes that render them ``useless'' in numerical computations.
  19. Piper M S: A Consistency Condition for the Double Series Approximation Method, Class. Quantum Grav. 14 (1997), 783. Also: Preprint gr-qc/9608001.
  20. Anninos P: Computational Cosmology: From the Early Universe to the Large Scale Structure, Max-Planck-Gesellschaft Living Reviews Series, No. 1998-9
  21. Anninos P, K Camarda, J Libson, J Massó, E Seidel, W-M Suen: Finding Apparent Horizons in Dynamic 3D Numerical Spacetimes, Phys. Rev. D 58 (1998), 024003. Also: Preprint gr-qc/9609059.
  22. Baumgarte T W, S L Shapiro: Numerical Integration of Einstein's Field Equations, Phys. Rev. D 59 (1998), 024007. Also: Preprint gr-qc/9810065.
  23. Frauendiener J: Numerical Treatment of the Hyperboloidal Initial Value Problem for the Vacuum Einstein Equations. I. The Conformal Field Equations, Phys. Rev. D 58 (1998), 064002. Also: Preprint gr-qc/9712050.
  24. Frauendiener J: Numerical Treatment of the Hyperboloidal Initial Value Problem for the Vacuum Einstein Equations. II. The Evolution Equations, Phys. Rev. D 58 (1998), 064003. Also: Preprint gr-qc/9712052.
  25. Seidel E: Numerical Relativity: Towards Simulations of 3D Black Hole Coalescence, gr-qc/9806088, Plenary talk given at GR15, Poona, India, to appear in the proceedings. Also: Preprint gr-qc/9806088.
  26. Stewart J M: The Cauchy Problem and the Initial Boundary Value Problem in Numerical Relativity, Class. Quantum Grav. 15 (1998), 2865
  27. Hübner P: How to Avoid Artificial Boundaries in the Numerical Calculation of Black Hole Spacetimes, Class. Quantum Grav. 16 (1999), 2145 (Paper I). Also: Preprint gr-qc/9804065.
  28. Hübner P: A Scheme to Numerically Evolve Data for the Conformal Einstein Equation, Class. Quantum Grav. 16 (1999), 2823 (Paper II) Also: Preprint gr-qc/9903088.
  29. Hern S D: Numerical Relativity and Inhomogeneous Cosmologies, PhD thesis, University of Cambridge, 1999, Preprint gr-qc/0004036.
  30. Frauendiener J: Numerical Treatment of the Hyperboloidal Initial Value Problem for the Vacuum Einstein Equations. III. On the Determination of Radiation, Class. Quantum Grav. 17 (2000), 373. Also: Preprint gr-qc/9808072.

Selected References
Last revision: Wes, 23-8-2000 (This page is under construction)