The point free Colombeau geometry in singular general relativity. Part II

Ja. Foukzon; A.A. Potapov; E.R. Men'kova

doi:10.18127/j20700970-202202-11

The point free Colombeau geometry in singular general relativity. Part II

Ja. Foukzon¹, A.A. Potapov², E.R. Men'kova³

research article UDC 530.12,531.134,537.9 Pages: 52-71 doi.org/10.18127/j20700970-202202-11

¹ Center for Mathematical Sciences, Israel Institute of Technology (Haifa, Israel)
² V.A. Kotel’nikov Institute of Radioengineering and Electronics of RAS (Moscow, Russia); Joint Chinese-Russian Laboratory of Informational Technologies and Signals Fractal Processing,
³ All-Russian Research Institute for Optical and Physical Measurements (Moscow, Russian)

Keywords: Singular Semi-Riemannian Geometry Colombeau Generalized Functions Colombeau Generalized Numbers Distribu-tional Schwarzschild Spacetime Point Free Distributional Geometry Generalized Einstein Field Equations Co-lombeau Solutions of the Einstein Field Equations

Abstract

Received: 16.11.2021
Approved after review: 02.12.2021
Accepted: 01.06.2022

How to cite

Фоукзон Дж., Потапов А.А., Менькова Е.Р. Точечно свободная геометрия Коломбо в сингулярной общей теории относительности // Нелинейный мир. 2022. Т. 20. № 2. С. 52-71. DOI: https://doi.org/10.18127/j20700970-202202-11

References

Foukzon J. British Journal of Mathematics & Computer Science. SCIENCEDOMAIN International. 20154 11(1): 1. Article no. BJMCS. 16961. DOI: https://doi.org/10.9734/BJMCS/2015/16961.
Foukzon J., Men'kova E. R., Potapov A.A. British Journal of Mathematics & Computer Science. 2016; 13(6): 1. Article no. BJMCS.19235. DOI: 10.9734/BJMCS/2016/19235.
Foukzon J., Men'kova E.R., Potapov A.A. Journal of High Energy Physics, Gravitation and Cosmology. 2018; 4(2). Paper ID 84304, 80 p. DOI: 10.4236/jhepgc.2018.42023.
Colombeau J. F. New Generalized Functions and Multiplication of Distributions. 1984. North Holland, Amsterdam.
Nedeljkov M., Pilipovic S., Scarpalezos D. Linear Theory of Colombeau Generalized Functions. London, United Kingdom. 01 Nov. 1998.
Grosser M., Kunzinger M., Oberguggenberger M., Steinbauer R. Geometric Theory of Generalized Functions with Applications to General Relativity. Netherlands. April 2013.
Biagioni H.A. A Nonlinear Theory of Generalized Functions. Springer. 14 Nov. 2006. Mathematics. 218 p.
Grosser M., Farkas E., Kunzinger M., Steinbauer R. On the Foundations of Nonlinear Generalized Functions I and II. Issue 729. American Mathematical Soc. 2001.
Rosinger E. E. Non-Linear Partial Differential Equations. Elsevier. 22 Nov. 1990.
Foukzon J., Men'kova E.R., Potapov A.A. Colombeau Solutions to Einstein Field Equations in General Relativity: Gravitational Singularities, Distributional SAdS BH Spacetime-Induced vacuum dominance. Book Publisher International l. Published Nov. 14. 2019. DOI: https://doi.org/10.9734/bpi/mono/978-93-89562-22-4.
Vernaeve H. Comm. Alg. 2010; 38(6): 2199. DOI: https://doi.org/10.1080/00927870903055222, arXiv:0707.0698 [math.RA]
Kunzinger M., Steinbauer R. Trans. Amer. Math. Soc. 2002; 354: 4179. DOI: https://doi.org/10.1090/S0002-9947-02-03058-1.
Grant J. D. E., Kunzinger M., Sämann C. Ann Glob Anal Geom (Dordr). 2019; 55(1): 133. DOI: 10.1007/s10455-018-9637-x.
Tozzi A. and Peters J.F. Br. J. Neurosci. Res. 2016; 94: 351.
Müller T., Grave F. arXiv: 0904.4184 [gr-qc] https://arxiv.org/abs/0904.4184v2.
Foukzon J., Men'kova E.R., Potapov A.A., Podosenov S.A. J. Phys.: Conf. Ser. 2018; 1141: 012100. DOI: https://doi:10.1088/1742-6596/1141/1/012100.

[1] Foukzon J. British Journal of Mathematics & Computer Science. SCIENCEDOMAIN International. 20154 11(1): 1. Article no. BJMCS. 16961. DOI: https://doi.org/10.9734/BJMCS/2015/16961.

[2] Foukzon J., Men'kova E. R., Potapov A.A. British Journal of Mathematics & Computer Science. 2016; 13(6): 1. Article no. BJMCS.19235. DOI: 10.9734/BJMCS/2016/19235.

[3] Foukzon J., Men'kova E.R., Potapov A.A. Journal of High Energy Physics, Gravitation and Cosmology. 2018; 4(2). Paper ID 84304, 80 p. DOI: 10.4236/jhepgc.2018.42023.

[4] Colombeau J. F. New Generalized Functions and Multiplication of Distributions. 1984. North Holland, Amsterdam.

[5] Nedeljkov M., Pilipovic S., Scarpalezos D. Linear Theory of Colombeau Generalized Functions. London, United Kingdom. 01 Nov. 1998.

[6] Grosser M., Kunzinger M., Oberguggenberger M., Steinbauer R. Geometric Theory of Generalized Functions with Applications to General Relativity. Netherlands. April 2013.

[7] Biagioni H.A. A Nonlinear Theory of Generalized Functions. Springer. 14 Nov. 2006. Mathematics. 218 p.

[8] Grosser M., Farkas E., Kunzinger M., Steinbauer R. On the Foundations of Nonlinear Generalized Functions I and II. Issue 729. American Mathematical Soc. 2001.

[9] Rosinger E. E. Non-Linear Partial Differential Equations. Elsevier. 22 Nov. 1990.

[10] Foukzon J., Men'kova E.R., Potapov A.A. Colombeau Solutions to Einstein Field Equations in General Relativity: Gravitational Singularities, Distributional SAdS BH Spacetime-Induced vacuum dominance. Book Publisher International l. Published Nov. 14. 2019. DOI: https://doi.org/10.9734/bpi/mono/978-93-89562-22-4.

[11] Vernaeve H. Comm. Alg. 2010; 38(6): 2199. DOI: https://doi.org/10.1080/00927870903055222, arXiv:0707.0698 [math.RA]

[12] Kunzinger M., Steinbauer R. Trans. Amer. Math. Soc. 2002; 354: 4179. DOI: https://doi.org/10.1090/S0002-9947-02-03058-1.

[13] Grant J. D. E., Kunzinger M., Sämann C. Ann Glob Anal Geom (Dordr). 2019; 55(1): 133. DOI: 10.1007/s10455-018-9637-x.

[14] Tozzi A. and Peters J.F. Br. J. Neurosci. Res. 2016; 94: 351.

[15] Müller T., Grave F. arXiv: 0904.4184 [gr-qc] https://arxiv.org/abs/0904.4184v2.

[16] Foukzon J., Men'kova E.R., Potapov A.A., Podosenov S.A. J. Phys.: Conf. Ser. 2018; 1141: 012100. DOI: https://doi:10.1088/1742-6596/1141/1/012100.

Abstract

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