Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dimensional analysis in relativity and in differential geometry   This note provides a short guide to dimensional analysis in Lorentzian and
general relativity and in differential geometry. It tries to revive Dorgelo and
Schouten's notion of 'intrinsic' or 'absolute' dimension of a tensorial
quantity. The intrinsic dimension is independent of the dimensions of the
coordinates and expresses the physical and operational meaning of a tensor. The
dimensional analysis of several important tensors and tensor operations is
summarized. In particular it is shown that the components of a tensor need not
have all the same dimension, and that the Riemann (once contravariant and
thrice covariant), Ricci (twice covariant), and Einstein (twice covariant)
curvature tensors are dimensionless. The relation between dimension and
operational meaning for the metric and stress-energy-momentum tensors is
discussed; and the possible conventions for the dimensions of these two tensors
and of Einstein's constant $\kappa$, including the curious possibility $\kappa
= 8\pi G$ without $c$ factors, are reviewed.

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The categories of this paper are: ao-sci
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: alg-geom
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The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
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The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
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The categories of this paper are: q-fin
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The categories of this paper are: bayes-an
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The categories of this paper are: eess
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The categories of this paper are: hep-lat
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The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex