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




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

Explore with Wolfram|Alpha


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.

Subject classifications