ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

11. Mathematical Physics

1991 MS Classification: 53, 83 Abdel-Megied, M., Minia University, El-Minia, Egypt, Buchner, K. , Technical University Munich, Germany, Gad Ragab M., Minia University, El-Minia, Egypt Conformal Singularities Let (M, g) be a space-time. Suppose there exists a manifold M̃ with boundary ∂M̃ such that

1. M̃ = M ∪ ∂M̃ and for each X ∈ ∂M̃ there exists a triple (Ũ, g̃, Ω), with Ũ an open neighborhood of X in M̃, g̃ a Lorentzian metric on Ũ, and Ω aC^{∞} a real valued function on Ũ such that

2. Ũ − ∂Ũ ∩ M and ∂Ũ = Ũ ∩ ∂M̃:

3. g = Ω^{2}g̃ on Ũ − ∂Ũ; Ω|∂Ũ = 0, Ω|(Ũ − ∂Ũ) > 0 and ∇Ω is no nowhere zero on Ũ. Then ∂M̃ is a conformal sigularity of (M, g). This definition due to Richard P. A. A. Newmann [2] is used to show that Friedmann singularity [1] is physical conformal singularity. It is proved also that if γ is an incomplete null geodesic terminating at conformal singularity of strongly causal space-time, then γ can be reparameterized, in a neighborhood of the conformal singularity, by an affine parameter to give a complete null geodesic. References [1] Belinski, V. A., Khalatnikov, I. M., and Lifschitz, E. M. (1982). “A General Solutions of the Einstein Equations with a Time Singularity”, Adv. Phys. 31, pp. 639 - 667. [2] Newmann, R. P. A. C. (1993). “On the Structure of Conformal Singularities in Classical General Relativity”, Proc. R. Soc. Lond. A 443, pp. 473 - 492.