Conformal Methods

1. Penrose R: Zero Rest-Mass Fields Including Gravitation: Asymptotic Behaviour, Proc. R. Soc. Lond. A 284 (1965), 159
   NB: (+ - - -), $\mu=0,\,1,\,2,\,3$, conformal invariance of zero rest-mass fields.
2. Penrose R: Structure of Space-Time, in Battelle Rencontres, eds. C M DeWitt, J A Wheeler, (New York: W A Benjamin Inc., 1968), 121
3. Schmidt B G: A New Definition of Conformal and Projective Infinity of Space-Times, Commun. Math. Phys. 36 (1974), 73
4. 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. Very technical. (+ - - -). Communicated by S W Hawking.
5. 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. Very technical. (+ - - -). Communicated by S W Hawking.
6. Goode S W, J Wainwright: Isotropic Singularities in Cosmological Models, Class. Quantum Grav. 2 (1985), 99
   NB: The introductory paper on their continued programme of investigations relating to "isotropic singularities" (cf.: Barrow 1978), "quiescent cosmology" and Penrose's Weyl curvature hypothesis (here: WTH). (- + + +).
7. Newman R P A C: On the Structure of Conformal Singularities in Classical General Relativity, Proc. R. Soc. Lond. A 443 (1993), 473
   NB: Provides arguments why "conformal singularity" should be preferred to "isotropic singularity". (+ - - -).
8. Baumgarte T W, S L Shapiro: Numerical Integration of Einstein's Field Equations, Phys. Rev. D 59 (1998), 024007. Also: Preprint gr-qc/9810065.
9. 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.
10. Friedrich H: Einstein's Equation and Conformal Structure, in The Geometric Universe: Science, Geometry and the Work of Roger Penrose, eds. S A Huggett, L J Mason, K P Tod, S S Tsou, N M J Woodhouse, (Oxford: Oxford University Press, 1998), 81
11. Anguige K, K P Tod: Isotropic Cosmological Singularities I. Polytropic Perfect Fluid Spacetimes, Ann. Phys. (N.Y.) 276 (1999), 257. Also: Preprint gr-qc/9903008.
    NB: $p(\mu) = (\gamma-1)\,\mu$, $1 < \gamma \leq 2$. (+ - - -).
12. 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.
13. Frauendiener J: Conformal Infinity, Max-Planck-Gesellschaft Living Reviews Series, No. 2000-4