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Positive Lightlike

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 lightlike if it has zero (Lorentzian) norm and if its first component v_0 is positive. Symbolically, v is positive lightlike if both

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

and

v_0>0

hold.

The collection of all positive lightlike vectors form the top half of the light cone.

See also

Light Cone, Lightlike, Lorentzian Inner Product, Lorentzian Space, Metric Signature, Negative Lightlike, Negative Timelike, Positive Timelike, 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 Lightlike." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/PositiveLightlike.html

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