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

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

and

v_0<0

hold.

The collection of all negative lightlike vectors form the bottom half of the light cone.

See also

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

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