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Volume 33: Pages 180-199, 2020
Singular general relativity using the Colombeau approach. I. Distributional Schwarzschild geometry from nonsmooth regularization via horizon
Jaykov Foukzon,1,a) Elena R. Men’kova,2 and Alexander A. Potapov3,4
1Center for Mathematical Sciences, Israel Institute of Technology, Haifa 3200003, Israel
2All-Russian Research Institute for Optical and Physical Measurements, Ozernaya Str. 46, Moscow 119361, Russia
3Kotelnikov Institute of Radioengineering and Electronics, Russian Academy of Sciences, Mokhovaya Str. 11, Building 7, Moscow 125009, Russia
4JNU-IREE Joint Laboratory of Fractal Method and Signal Processing, Department of Electronic Engineering, College of Information Science and Technology, Jinan University, Guangzhou, China
We studied the Schwarzschild solution using Colombeau distributional geometry [M. Kunzinger and R. Steinbauer, Trans. Am. Math. Soc. 354, 4179 (2002)], thus without leaving Schwarzschild coordinates
Nous avons étudié la solution de Schwarzschild en utilisant la géométrie distributionnelle de Colombeau [M. Kunzinger, R. Steinbauer, Trans. Amer. Math. Soc. 354, 4179 (2002). https://doi.org/10.1090/S0002-9947-02-03058-1], donc sans laisser les coordonnées de Schwarzschild.
Key words: Singular Semi-Riemannian Geometry; Colombeau Generalized Functions; Colombeau Generalized Numbers; Distributional Schwarzschild Spacetime; Point Free Distributional Geometry; Generalized Einstein Field Equations; Colombeau Solutions of the Einstein Field Equations.
Received: March 21, 2017; Accepted: April 12, 2020; Published Online: May 5, 2020