Vol. 9, no.2, 2017


Sergey A. Podosenov, Elena R. Men'kova
All-Russian Research Institute for Optical and Physical Measurements, http://www.vniiofi.ru
Moscow 119361, Russian Federation
Alexander A. Potapov
Kotel’nikov Institute of Radioengineering and Electronics, Russian Academy of Sciences, http://www.cplire.ru
Moscow 125009, Russian Federation
Jinan University, College of Information Science and Technology/College of Cyber Security, http://www. jnu.edu.cn
Guangzhou 510632, China
Cooperative Chinese-Russian Laboratory of Informational Technologies and Signals Fractal Processing, Guangzhou 510632, China
Jaykov Foukzon
Center for Mathematical Sciences, Israel Institute of Technology, http://www.technion.ac.il

podosenov@mail.ru, potapov@cplire.ru, jaykovfoukzon@list.ru, e_menkova@mail.ru

Abstract. A continuum motion in the flat Minkowski space in the specified force field is considered. When movement the relative space-time curvature stipulated by the noncoincidence of the hypersurface orthogonal to world lines of basis particles with the simultaneity hypersurface arises. The anholonomic mathematical apparatus and its continua application is developed. Metrics for relative 4-interval element squares for the arbitrary continuum motion and special cases are found. The acceleration addition law is obtained. It turns out that exact solutions of the Einstein’s equations for the isotropic cosmological model for the strongly evacuated gas and for the critical density follow from solutions of the Newtonian gas dynamics Euler’s equations.

Keywords: space-time, curvature tensor, reference frame, Born's rigidity, Minkowski, Riemann, Einstein, coordinates, Christoffel, hypersurfaces

UDC 530.12, 531.134, 537.9c

Bibliography – 25 references
Received 10.11.2017

RENSIT, 2017, 9(1):161-180 DOI: 10.17725/rensit.2017.09.161

Full-text electronic version of this article - web site http://en.rensit.ru/vypuski/article/219/9(2)161-180e.pdf