Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: When is g_{tt} g_{rr} = -1?   The Schwarzschild metric, its Reissner-Nordstrom-de Sitter generalizations to
higher dimensions, and some further generalizations all share the feature that
g_{tt} g_{rr}=-1 in Schwarzschild-like coordinates. In this pedagogical note we
trace this feature to the condition that the Ricci tensor (and stress-energy
tensor in a solution to Einstein's equation) has vanishing radial null-null
component, i.e. is proportional to the metric in the t-r subspace. We also show
this condition holds if and only if the area-radius coordinate is an affine
parameter on the radial null geodesics.

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The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas
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The categories of this paper are: math-ph
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The categories of this paper are: econ
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The categories of this paper are: nlin
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The categories of this paper are: hep-lat
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The categories of this paper are: atom-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: chem-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: acc-phys
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: solv-int
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The categories of this paper are: q-fin