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Minkowski geometry and space-time manifold in relativity

Author

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  • Mohajan, Haradhan

Abstract

Space-time manifold plays an important role to express the concepts of Relativity properly. Causality and space-time topology make easier the geometrical explanation of Minkowski space-time manifold. The Minkowski metric is the simplest empty space-time manifold in General Relativity, and is in fact the space-time 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 space-time 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.

Suggested Citation

  • Mohajan, Haradhan, 2013. "Minkowski geometry and space-time manifold in relativity," MPRA Paper 51627, University Library of Munich, Germany, revised 03 Nov 2013.
    • Handle: RePEc:pra:mprapa:51627
    as

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    File URL: https://mpra.ub.uni-muenchen.de/51627/1/MPRA_paper_51627.pdf
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    References listed on IDEAS

    as
    1. Mohajan, Haradhan, 2013. "Schwarzschild Geometry from Exact Solution of Einstein Equation," MPRA Paper 50795, University Library of Munich, Germany, revised 16 Oct 2013.
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    Citations

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    Cited by:

    1. Mohajan, Haradhan, 2016. "Singularities in Global Hyperbolic Space-time Manifold," MPRA Paper 82953, University Library of Munich, Germany, revised 16 Mar 2016.
    2. Mohajan, Haradhan, 2015. "Basic Concepts of Differential Geometry and Fibre Bundles," MPRA Paper 83002, University Library of Munich, Germany, revised 18 Feb 2015.
    3. Vitor H. Carvalho & Raquel M. Gaspar, 2021. "Relativistically into Finance," Working Papers REM 2021/0175, ISEG - Lisbon School of Economics and Management, REM, Universidade de Lisboa.
    4. Vitor H. Carvalho & Raquel M. Gaspar, 2021. "Relativistic Option Pricing," IJFS, MDPI, vol. 9(2), pages 1-24, June.

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    More about this item

    Keywords

    Causal structure; Geodesics; Ideal points; Minkowski metric; Space-time manifold;
    All these keywords.

    JEL classification:

    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables

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