Mohajan, Haradhan (2013): Minkowski geometry and spacetime manifold in relativity. Published in: Journal of Environmental Treatment Techniques , Vol. 1, No. 2 (10 November 2013): pp. 101109.

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Abstract
Spacetime manifold plays an important role to express the concepts of Relativity properly. Causality and spacetime topology make easier the geometrical explanation of Minkowski spacetime manifold. The Minkowski metric is the simplest empty spacetime manifold in General Relativity, and is in fact the spacetime of the Special Relativity. Hence it is the entrance of the General Relativity and Relativistic Cosmology. No material particle can travel faster than light. So that null space is the boundary of the spacetime manifold. Einstein equation plays an important role in Relativity. Some related definitions and related discussions are given before explaining the Minkowski geometry. In this paper an attempt has been taken to elucidate the Minkowski geometry in some details with easier mathematical calculations and diagrams where necessary.
Item Type:  MPRA Paper 

Original Title:  Minkowski geometry and spacetime manifold in relativity 
English Title:  Minkowski geometry and spacetime manifold in relativity 
Language:  English 
Keywords:  Causal structure, Geodesics, Ideal points, Minkowski metric, Spacetime manifold 
Subjects:  C  Mathematical and Quantitative Methods > C3  Multiple or Simultaneous Equation Models ; Multiple Variables 
Item ID:  51627 
Depositing User:  Haradhan Kumar Mohajan 
Date Deposited:  22 Nov 2013 05:37 
Last Modified:  15 Jan 2017 11:30 
References:  1 Hawking S.W., Ellis, G.F.R., The Large Scale Structure of Spacetime, Cambridge University Press, Cambridge. 1973. 2 Joshi P.S., Global Aspects in Gravitation and Cosmology, Clarendon Press, Oxford. 1993. 3 Lipschutz, S., General Topology, Schum’s Outline Series, Singapore, 1st edition, 1965. 4 Mohajan H.K., Singularity Theorems in General Relativity, M. Phil. Dissertation, Lambert Academic Publishing, Germany. 2013. 5 Mohajan H.K., Schwarzschild Geometry from Exact Solution of Einstein Equation, Journal of Environmental Treatment Techniques, 2013. 1(2): 69–75. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/51627 