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Positive Timelike

A nonzero vector v=(v_0,v_1,...,v_(n-1)) in n-dimensional Lorentzian space R^(1,n-1) is said to be positive timelike if it has imaginary (Lorentzian) norm and if its first component v_0 is positive. Symbolically, v is positive timelike if both

-v_0^2+v_1^2+...+v_(n-1)^2<0

and

v_0>0

hold. Note that equation (6) above expresses the imaginary norm condition by saying, equivalently, that the vector v has a negative squared norm.

See also

Light Cone, Lightlike, Lorentzian Inner Product, Lorentzian Space, Metric Signature, Negative Lightlike, Negative Timelike, Positive Lightlike, Spacelike, Timelike

This entry contributed by Christopher Stover

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References

Misner, C. W.; Thorne, K. S.; and Wheeler, J. A. Gravitation. San Francisco, CA: W. H. Freeman, p. 53, 1973.Ratcliffe, J. G. Foundations of Hyperbolic Manifolds. New York: Springer-Verlag, 2006.

Cite this as:

Stover, Christopher. "Positive Timelike." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/PositiveTimelike.html

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