Basic Vectors in Relativity

  • David A. de Wolf Virginia Tech (retired)


Basis vectors e(_alpha) play a useful role in special and general relativity. In particular they allow an expansion of the vectorial spacetime interval ds along infinitesimal curvilinear coordinate differences: ds = e(_alpha)(unit-xi), thus the conventional definition Usually a second coordinate system is needed to obtain explicit expressions for basis vectors. In this work, single-coordinate-system expressions for basis vectors [Eqs. (10) and (14)] are derived. Applications to nonorthogonal coordinate systems are worked out.


Bergmann, P. G. (1976). Introduction to the Theory of Relativity. Courier Corporation.
Hartle, J. B. (2003). Gravity: an introduction to Einstein’s general relativity. Pearson Education, Inc.
Hobson, M.P., Efstathiou, G. and Lasenby, A.N. (2006). General Relativity, An Introduction for Physicists, Cambridge University Press.
Misner, C.W., Thorne, K.S. and Wheeler, J.A. (1984). Gravitation, W.H. Freeman, Princeton, University Press.
Schutz, B. (2009). A first course in general relativity. Cambridge university press.
How to Cite
DE WOLF, David A.. Basic Vectors in Relativity. European Journal of Physics Education, [S.l.], v. 12, n. 1, p. 15-23, mar. 2021. ISSN 1309-7202. Available at: <>. Date accessed: 20 july 2024.
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