https://en.wikipedia.org/wiki/Clifford_algebra

In general relativity, Kruskal–Szekeres coordinates, named after Martin Kruskal and George Szekeres, are a coordinate system for the Schwarzschild geometry for a black hole. These coordinates have the advantage that they cover the entire spacetime manifold of the maximally extended Schwarzschild solution and are well-behaved everywhere outside the physical singularity. There is no coordinate singularity at the horizon.

The Kruskal–Szekeres coordinates also apply to space-time around a spherical object, but in that case do not give a description of space-time inside the radius of the object. Space-time in a region where a star is collapsing into a black hole is approximated by the Kruskal–Szekeres coordinates (or by the Schwarzschild coordinates). The surface of the star remains outside the event horizon in the Schwarzschild coordinates, but crosses it in the Kruskal–Szekeres coordinates. (In any “black hole” which we observe, we see it at a time when its matter has not yet finished collapsing, so it is not really a black hole yet.) Similarly, objects falling into a black hole remain outside the event horizon in Schwarzschild coordinates, but cross it in Kruskal–Szekeres coordinates.

https://en.wikipedia.org/wiki/Kruskal%E2%80%93Szekeres_coordinates

Tensor Rank

The total number of contravariant and covariant indices of a tensor. The rank  of a tensor is independent of the number of dimensions  of the underlying space.

An intuitive way to think of the rank of a tensor is as follows: First, consider intuitively that a tensor represents a physical entity which may be characterized by magnitude and multiple directions simultaneously (Fleisch 2012). Therefore, the number of simultaneous directions is denoted  and is called the rank of the tensor in question. In -dimensional space, it follows that a rank-0 tensor (i.e., a scalar) can be represented by  number since scalars represent quantities with magnitude and no direction; similarly, a rank-1 tensor (i.e., a vector) in -dimensional space can be represented by  numbers and a general tensor by  numbers. From this perspective, a rank-2 tensor (one that requires  numbers to describe) is equivalent, mathematically, to an  matrix.

rankobject0scalar1vector2 matrixtensor

The above table gives the most common nomenclature associated to tensors of various rank. Some care must be exhibited, however, because the above nomenclature is hardly uniform across the literature. For example, some authors refer to tensors of rank 2 as dyads, a term used completely independently of the related term dyadic used to describe vector direct products (Kolecki 2002). Following such convention, authors also use the terms triad, tetrad, etc., to refer to tensors of rank 3, rank 4, etc.

Some authors refer to the rank of a tensor as its order or its degree. When defining tensors abstractly by way of tensor products, however, some authors exhibit great care to maintain the separation and distinction of these terms

https://mathworld.wolfram.com/TensorRank.html