However, when discussing causal horizons, trapped null surfaces are defined as only null vector fields giving rise to null surfaces.
12.
The same reversed form of the inequality holds if both vectors lie in the past light cone, and if one or both are null vectors.
13.
All this radiation is traveling in the same direction, and the null vector k = \ partial _ v plays the role of a wave vector.
14.
The four linearly independent biquaternions,,, and are null vectors and } } can serve as a basis for the subspace used to represent spacetime.
15.
This possibility is a tensor analogue of the well known that a null vector always has vanishing length, even if it is not the zero vector.
16.
For example, one can easily construct a ( non-orthonormal ) basis consisting entirely of null vectors, called a "'null basis " '.
17.
However, allowing complex numbers, one can obtain a null tetrad, which is a basis consisting of null vectors, some of which are orthogonal to each other.
18.
Though the term " metric " is used in cosmology, the fundamental idea is different because there are non-zero null vectors in the tangent space of these manifolds.
19.
Parabolic Lorentz transformations are often called "'null rotations "', since they preserve null vectors, just as rotations preserve timelike vectors and boosts preserve spacelike vectors.
20.
If you view the Riemann tensor as a second rank tensor acting on bivectors, the vanishing of invariants is analogous to the fact that a nonzero null vector has vanishing squared length.
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