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A vector is timelike if c 2 t 2 > r 2, spacelike if c 2 t 2 < r 2, and null or lightlike if c 2 t 2 = r 2. This can be expressed in terms of the sign of η(v, v), also called scalar product, as well, which depends on the signature. The classification of any vector will be the same in all frames of reference that are related by a Lorentz ...
Geodesics are said to be timelike, null, or spacelike if the tangent vector to one point of the geodesic is of this nature. Paths of particles and light beams in spacetime are represented by timelike and null (lightlike) geodesics, respectively. [64]
The difference (or interval) between two events can be classified into spacelike, lightlike and timelike separations. Only if two events are separated by a lightlike or timelike interval can one influence the other.
causal (or non-spacelike) if the tangent vector is timelike or null at all points in the curve. The requirements of regularity and nondegeneracy of Σ {\displaystyle \Sigma } ensure that closed causal curves (such as those consisting of a single point) are not automatically admitted by all spacetimes.
Again the metric defines lightlike (null), spacelike, and timelike curves. Also, in general relativity, world lines include timelike curves and null curves in spacetime, where timelike curves fall within the lightcone. However, a lightcone is not necessarily inclined at 45 degrees to the time axis.
In theoretical physics, null infinity is a region at the boundary of asymptotically flat spacetimes.In general relativity, straight paths in spacetime, called geodesics, may be space-like, time-like, or light-like (also called null).
A maximally symmetric Lorentzian manifold is a spacetime in which no point in space and time can be distinguished in any way from another, and (being Lorentzian) the only way in which a direction (or tangent to a path at a spacetime point) can be distinguished is whether it is spacelike, lightlike or timelike.
A four-vector A is a vector with a "timelike" component and three "spacelike" components, and can be written in various equivalent notations: [3] = (,,,) = + + + = + = where A α is the magnitude component and E α is the basis vector component; note that both are necessary to make a vector, and that when A α is seen alone, it refers strictly to the components of the vector.